Bar Salibi writes quite a lot about the sign of the cross in the 12th century.
You write :"The sacrament of the sign of the cross consists in the Word of God who became flesh and came down from heaven to earth, and removed mankind from the left hand and darkness to the right hand and light."
We do not drive away darkness with light, as you write, by making the sign of the cross from right to left ; everyone knows that darkness is the very antithesis of light, and that if the latter is mixed up in the former it becomes swallowed up in it in the same way as the bitterness of a little brackish water in a jug of sweet water, or that of a little myrrh or wormwood in a considerable quantity of honey. Let us admit that light drives away darkness, how can the left hand drive away the right ? Our Lord has said that He will set the sheep on His right hand and the goats on His left ; in this our Saviour demonstrated that the right cannot expel the left, but those who make the sign of the cross from right to left, move, out of their own free will, from the right hand to the left which is that of the goats, and are counted with the robber who was on our Lord's left.
But see how in the consecration of the elements and in the final prayers of the service the Greeks make the sign of the cross like us, from left to right, and in this way they contradict themselves.
You write : "Is it not more advantageous that a man should cross himself in beginning with the right side, which is the side of light, and then pass this light over his face and with it drive away darkness, than to cross himself from the side of darkness and pass it over his face ?"
If darkness and light are defined by the right hand moving horizontally, tell me what is meant by the first act we do in crossing ourselves, which consists in moving our hand in a perpendicular way from our head downwards ? You might say that the top movement means light and the bottom one darkness, and that a man first takes light and comes down to darkness, and then takes light again to another darkness. The Greeks would have thus two lights and two darknesses, and would begin with light and end with darkness. This theory of yours is not a happy one, and the single cross is not light in one of its horizontal sides and darkness in the other, but it is light in both of its sides. It is also advantageous that the end of all our works should be on the right hand, that is to say, good, and it is thus better to end the sign of the cross with the side of the right hand, and not with the side of the left which is, according to the words of our Lord, that of the goats.
In administering the baptism even the Greeks make the sign of the cross on the child with a collyrium-pencil which has one point only and not two points, which would correspond with the two fingers, and move also the instrument from left to right as we do, and not from right to left. Had they not done so in this case even their cross would not have been straight but twisted.
This does not explain the divergent practice, but it seems to be of some great antiquity as far as Bar Saliba is concerned.