One of my favorite subjects -
I have a special personal attachment to the Magi (I've always wondered why the Magi aren't emphasized more in our traditions, seeing that they were "of the East" and, logically therefore - to my mind at least, should peculiarly "belong" to our Churches - though, admittedly, the Oriental Orthodox and Catholics do give them more attention).
The Magi are inextricably tied to my earliest recollection of understanding compass directions. Our downstairs neighbors were a childless Greek couple. She had no real charm about her (nor any personality), but her husband, Dr. K, of blessed memory, was a delightful man who was a veritable fount of information generally considered useless, but invaluable to children. He would come upstairs with his compass and he and my Dad would make a great show of calculating East to assure proper direction for the Magi, who were always off to the side - out of sight of the stable until Epiphany, when they would be marched up into place. I was continually amazed that each year East was in the same place

"Manger scenes", as they are typically erected, should probably be considered as man's effort to visualize an event about which we have very limited information available, in that they likely compress events into a single scene. (I am no biblical scholar, so please forgive me any mis-statements in what follows)
Luke speaks of the shepherds being informed by the angel that the birth occurred that very day and he says that they found the Baby in a manger. Matthew's account of the circumstances involving the Magi is less precisely fixed. His Gospel only describes the birth, and (by inference from the meeting between them and Herod) the Magi's visit, as occuring during the time of Herod.
Given that we have no evidence for how long a period elapsed before the Family fled to Egypt, it's not unreasonable to conclude that they may have resided for some period in Bethlehem prior to departing. That period could have been anywhere from the two weeks that, in real time, would account for dating the Magi's visit as having been in January. That it might have been even longer could be inferred from Herod's caution in ordering the killing of all infant boys aged two or younger, to be certain that he covered all possibilities.
The latter suggests that the Magi, in their initial conversation with him, were uncertain as to the actual date on which the Child was born. Not unreasonable - I don't know that anyone has ever firmly established that either the prophecies on which they relied or their actual observation of the Star was tied in time to the Birth itself or was a portent of its future happening - allowing them time to arrive and be present at it. The latter seems unlikely because of the differences between Luke and Matthew in relating the matters of the Birth and the Magi's arrival.
Since one can presume that the Star which guided them was visible from the inception of their journey until its conclusion, I suppose one could look to some of the works that have been written over the years regarding the visibility of various heavenly bodies that have been proposed as the Star of Bethlehem. I would be surprised if none of those treatises have indicated the period of time during which the Star would have been visible. Such might suggest how long the travelers followed it.
The placement of the Magi in the stable or cave scene itself, whether on Christmas Day or Epiphany, is almost certainly a convenience to human understanding. It offers the symbolic statement that Christ's birth was for all mankind, the poor and low-born shepherds and the rich, high-born, and educated Magi, as well as the choirs of Heaven. It would be much more difficult to convey that same understanding if the Magi's arrival were separated entirely from the visualization of Christmas morning.
If you think about it, most of those traveling to Bethlehem for the census likely left shortly after and lodging would have been more readily available. One can surmise that Mary, Joseph, and the Baby had relocated to someplace more hospitable than the cave or stable, as soon as possible after Jesus' Birth.
In essence, we'll never know with complete certainty, as least not in this life, just as we don't know precisely how many the Magi were in number. Caspar/Gaspar, Melchior, and Balthazar are traditionally named, but folks have put other names to them. The Ethiopians speak of Hor, Basanater, and Karsudan - but put the total number as 13, as I recollect; the Syrians nominate them as Larvandad, Hormisdas, and Gushnasaph; to the Armenians they were, anciently, Kagba, Badadilma, and Melkon.
More diverse than the names are the various numbers of them; they are depicted in various representations and traditions as being as few as 2 and as many as 14. The number 3 is most likely ascribed from the number of gifts they offered.
Many cultures have folktales that tell of someone (other than the expected entourage of guards, servants, etc.) who was supposed to travel with the Magi, but was prevented from doing so, by some circumstance or other, usually with consequences. Such "wannabe" Magi are usually associated thereafter with gift-giving, at either Christmas or Epiphany, in their endless search for the Child.
Along this line, in Italy, one finds "La Befana", a kindly old witch. Legend says that she lived alone in the hills. She noticed a bright star in the night sky; later, 3 richly garbed men stopped and asked directions to Bethlehem. When she said that she didn't know of any such a place, they invited her to join them in their search; she declined, as she was too busy.
After the Magi left, Befana suffered regrets about her choice, remembering her own child, who died very young. She baked cakes and cookies for the Baby, took her broom (to help the Baby's mother clean), and set out to find the caravan. When she became lost and tired, angels appeared and gave her broom the power of flight, to speed her search. She roamed the world, hunting for the Baby and still does. And each year, on the eve of Epiphany, whenever Befana comes to a house where there is a child, she flies down the chimney to see if it might be the One she seeks. It never is, but she leaves a gift anyway.
Henry van Dyke, an early 20th century writer, crafted a short story, "The Other Wise Man", which related another legend. In it, Artaban, a fourth Magi, was late in arriving to meet the others, who had already left. By the time he came to Bethlehem, they and the Holy Family had left to flee Herod's wrath. Artaban wandered the earth for 33 years, searching and using his gifts (jewels) to benefit others. When he encountered Christ, face-to-face, on Golgotha, his fortune was gone and he wasn't able to ransom Him. As Christ died and earth was shaken by a quake, Artaban was struck by a stone falling from a building. As he lay dying, he heard a voice from Heaven, saying, "What you did for each of these, you did for Me."
Babushka, an elderly Russian folklore character, appears in two variants of such tales. One mirrors the Italian tale of the initially selfish and later repentant La Befana; the other is a variant on van Dyke's story, except that Babushka reaches the stable, sorrowing that she has given away all her gifts and is consoled to find that what she did for others, she did for the Baby.
Among both the "Saint Thomas Christians" of India (Malabarese and Malankarese Catholics and Orthodox) and the Chaldeans and Assyrians (where the Magi likely had their roots), legend has the Magi encounter the Apostle Thomas some forty years later, when he arrived in their lands to evangelize. According to tradition, the three, then elderly, were converted and ordained, dying shortly afterwards.
The feasts of Saints Caspar, Melchior, and Balthazar are kept in the Coptic, Ethiopian, Eritrean, Chaldean, Assyrian, Malabarese, and Malakarese Churches on January 1, 6, and 11, respectively.
The relics of the Magi are believed to be enshrined in the magnificent Cathedral of Cologne, which was constructed specifically to provide a suitable repository for them.
The Troparion of Christmas in the Liturgy of Saint John Chrysostom, used in Eastern Catholic Churches of the Byzantine Rite and in the Eastern Orthodox Churches, reads in part:
Your birth, O Christ our God, has shed upon the world the light of knowledge; for through it those who worshipped the stars have learned from a star to worship You, the Sun of Justice, and to recognize You as the Orient From On High. Glory be to You, O Lord!
I had the privilege as a college student of briefly knowing Father Francis X. Weiser, SJ, of blessed memory.
Father was, among other things (e.g., chaplain to the von Trapp family), an Austrian-American Jesuit and a renowned student of Christian folklore and customs. In one of his writings about Christmas customs, this is what he had to offer about the Magi:
The Magi -- The name "magi" is not a Hebrew word but of Indo-Germanic origin, meaning "great, illustrious." St. Matthew mentions the term without explanation because it was well known to the people of Palestine. The Magi originated in Media (Persia) and their caste later spread to other oriental countries. They were a highly esteemed class of priestly scholars, devoting themselves not only to religion but also to the study of natural sciences, medicine, mathematics, astronomy, and astrology. In several countries they were members of the king's council.
Quite early in the Christian era a popular tradition conferred on the Magi of Bethlehem the title of kings. This tradition became universal at the end of the sixth century. It was based on Biblical prophecies which described the conversion of the pagans and, although not referring to the Magi, was applied to their visit, as, for instance, in the following texts:
"The kings of Tharsis and the islands shall offer presents: the kings of the Arabians and of Saba shall bring gifts."--Psalm 71,10.
"The kings shall walk in the brightness of thy rising....They all shall come from Saba, bringing gold and frankincense." --Isaias 60, 3-6.
Where did the Magi come from? St. Matthew gives a general answer: "Wise men from the East." Was it Persia or Arabia? Speaking in modern terms, it could have been any one of the countries of Arabia, Iraq, Iran, Afghanistan, or India. It has never been exactly determined from which of these countries they came.
Neither has their exact number ever been established. The Gospel does not tell us how many they were. The Christians in the Orient had a tradition of twelve Magi. In early paintings and mosaics they are represented as two, three, four and even more. In the occidental church a slowly spreading tradition put their number at three. This tradition became universal in the sixth century. It does not seem to have any historical foundation but was probably based on the fact of the threefold presents which the Magi offered. Another reason for the number three was the early legend that they were representing all humanity in the three great races of Sem, Cham, and Japhet. This particular legend is also the reason for picturing one of the three as a member of the black race.
The book "Collectanea et Flores," ascribed to St. Bede the Venerable (735), records an early legend of their names and appearance: "The first was called Melchior; he was an old man, with white hair and long beard; he offered gold to the Lord as to his king. The second, Gaspar by name, young, beardless, of ruddy hue, offered to Jesus his gift of incense, the homage due to Divinity. The third, of black complexion, with heavy beard, was called Baltasar; the myrrh he held in his hands prefigured the death of the Son of man."[8]
There is an old legend that when many years had passed the Magi were visited by St. Thomas the Apostle, who after instructing them in Christianity, baptized them. They were then ordained to the priesthood and later made bishops. It is said that once more the star of Bethlehem appeared to them--reunited them toward the end of their lives. "The city of Sewa in the Orient" is given as the place of their burial.[9] The legendary relics of the Magi were brought to Constantinople in the fifth century; one hundred years later they were transferred to Milan, and in 1164 to Cologne under Emperor Barbarossa (1190). Their shrine in Cologne was, and still is, the center of many pilgrimages
endnotes:
8. "Sanctus Beda Venerabilis De Collectaneis" (Collected Notes). J. P. Migne, "Patrologia Latina," vol. XCIV, col. 541.
9. "Divine Office," Proprium of the Archdiocese of Cologne, Feast of the Translation of the Magi (July 23rd), second Nocturn.
Many years,
Neil