Greetings in that Divine and Most Precious Name of Our Lord and Savior Jesus Christ!
The Ethiopians have a veneration towards him based on the content of various Apocryphal works.
Actually the Ethiopian Orthodox Tewahedo Church bases the veneration of St Pontius Pilate on his confession at the Trial of Christ in the Gospels. The Ethiopian Fathers' writings and commentaries elaborate based on the Gospels the deep significance in connection with the Prophets and the Psalms the witnessing and confession of St Pontius Pilate. We have had this discussion before on the forum, and folks mistakenly assume that the Sainthood of Pontius Pilate in the Tewahedo Church was based on as you mention, pseudo-canonical Scriptures about Pilate's guilt trip and post-Crucifixion repentance, however this is not why the Ethiopians have Sainted the man. I'm not even sure if the Ethiopians traditionally ever had any of these Epistles of Pontius Pilate [http://www.interfaith.org/christianity/apocrypha-epistles-of-pontius-pilate/] or the Confessions of Pontius Pilate which float around today as Apocryphal.
From the Ethiopian Synaxarium
Senne 25(July 02) On this day also died Pilate, the confessor. Salutation to Pilate who washed his hands of
the Blood of Jesus Christ.
The Fathers have then elaborated that it was in the insisting to release Our Lord and then ultimately washing his hands of the whole affair, then issuing the decree "King of the Jews" on the Cross, St. Pontius Pilate then both was not guilty of Our Lord and also confessed before the people that our Lord was indeed the King.
11 Meanwhile Jesus stood before the governor, and the governor asked him, “Are you the king of the Jews?”
“You have said so,” Jesus replied.
12 When he was accused by the chief priests and the elders, he gave no answer. 13 Then Pilate asked him, “Don’t you hear the testimony they are bringing against you?” 14 But Jesus made no reply, not even to a single charge—to the great amazement of the governor.
15 Now it was the governor’s custom at the festival to release a prisoner chosen by the crowd. 16 At that time they had a well-known prisoner whose name was Jesus Barabbas. 17 So when the crowd had gathered, Pilate asked them, “Which one do you want me to release to you: Jesus Barabbas, or Jesus who is called the Messiah?” 18 For he knew it was out of self-interest that they had handed Jesus over to him.
22 “What shall I do, then, with Jesus who is called the Messiah?” Pilate asked.
They all answered, “Crucify him!”
23 “Why? What crime has he committed?” asked Pilate.
But they shouted all the louder, “Crucify him!”
24 When Pilate saw that he was getting nowhere, but that instead an uproar was starting, he took water and washed his hands in front of the crowd. “I am innocent of this man’s blood,” he said. “It is your responsibility!”
25 All the people answered, “His blood is on us and on our children!”
Matthew 27 NIV
9 “Do you want me to release to you the king of the Jews?” asked Pilate, 10 knowing it was out of self-interest that the chief priests had handed Jesus over to him. 11 But the chief priests stirred up the crowd to have Pilate release Barabbas instead.
12 “What shall I do, then, with the one you call the king of the Jews?” Pilate asked them.
13 “Crucify him!” they shouted.
14 “Why? What crime has he committed?” asked Pilate
Mark 15 NIV
So Pilate asked Jesus, “Are you the king of the Jews?”
“You have said so,” Jesus replied.
4 Then Pilate announced to the chief priests and the crowd, “I find no basis for a charge against this man.”
Pilate called together the chief priests, the rulers and the people, 14 and said to them, “You brought me this man as one who was inciting the people to rebellion. I have examined him in your presence and have found no basis for your charges against him. 15 Neither has Herod, for he sent him back to us; as you can see, he has done nothing to deserve death. 16 Therefore, I will punish him and then release him.”  [a]
18 But the whole crowd shouted, “Away with this man! Release Barabbas to us!” 19 (Barabbas had been thrown into prison for an insurrection in the city, and for murder.)
20 Wanting to release Jesus, Pilate appealed to them again. 21 But they kept shouting, “Crucify him! Crucify him!”
22 For the third time he spoke to them: “Why? What crime has this man committed? I have found in him no grounds for the death penalty. Therefore I will have him punished and then release him.”
Once more Pilate came out and said to the Jews gathered there, “Look, I am bringing him out to you to let you know that I find no basis for a charge against him.” 5 When Jesus came out wearing the crown of thorns and the purple robe, Pilate said to them, “Here is the man!”
6 As soon as the chief priests and their officials saw him, they shouted, “Crucify! Crucify!”
But Pilate answered, “You take him and crucify him. As for me, I find no basis for a charge against him.”
7 The Jewish leaders insisted, “We have a law, and according to that law he must die, because he claimed to be the Son of God.”
8 When Pilate heard this, he was even more afraid, 9 and he went back inside the palace. “Where do you come from?” he asked Jesus, but Jesus gave him no answer. 10 “Do you refuse to speak to me?” Pilate said. “Don’t you realize I have power either to free you or to crucify you?”
11 Jesus answered, “You would have no power over me if it were not given to you from above. Therefore the one who handed me over to you is guilty of a greater sin.”
12 From then on, Pilate tried to set Jesus free, but the Jewish leaders kept shouting, “If you let this man go, you are no friend of Caesar. Anyone who claims to be a king opposes Caesar.”
13 When Pilate heard this, he brought Jesus out and sat down on the judge’s seat at a place known as the Stone Pavement (which in Aramaic is Gabbatha). 14 It was the day of Preparation of the Passover; it was about noon.
“Here is your king,” Pilate said to the Jews.
15 But they shouted, “Take him away! Take him away! Crucify him!”
“Shall I crucify your king?” Pilate asked.
Pilate had a notice prepared and fastened to the cross. It read: JESUS OF NAZARETH, THE KING OF THE JEWS. 20 Many of the Jews read this sign, for the place where Jesus was crucified was near the city, and the sign was written in Hebrew, Latin and Greek. 21 The chief priests of the Jews protested to Pilate, “Do not write ‘The King of the Jews,’ but that this man claimed to be king of the Jews.”
22 Pilate answered, “What I have written, I have written.”
There are three specific aspects to Saint Pontius Pilate's confession according to the Tewahedo Church Fathers (hence why he is known as Saint Pontius Pilate the Confessor)
1) When he reiterated to the people the innocence of Jesus Christ, and specifically washed his hands publically of the whole affair, which is memorialized at each Divine Liturgy when the celebrating priest washes his hands of the blood guilt of any of those approaching the Altar to commune in a state of sin.
2) When he said to the people "Here is the Man" he was acknowledging the perfect humanity of Jesus Christ (Christology) and when he said "Here is the King of Israel" he was acknowledging Jesus Christ as the messiah. Now as to the perfect divinity of Jesus Christ, some Ethiopian Fathers attest that Pilate recognized Jesus indeed as God Incarnate which was why it is said in the Gospel of John that Pilate became afraid and also why he heeded the dreams and visions of his wife's warning.
3) When he refused to heed the requests to change the indictment on the Cross, indeed the indictment which read in Greek, Latin, and Hebrew (which is actually quite theological because the Jews then spoke Aramaic, Hebrew was a liturgical/theological language like Latin to the Catholics and Slavic to the Russians and Ge'ez to the Ethiopians) Jesus of Nazareth, King of the Jews, is Pilate's Confession. In the Gospel of John it explains that Pilate himself personally arranged that indictment and what was written and said, "What I have written I have written!"