La cohorte et le tribun se saisirent de Jésus, le lièrent et le menèrent au prétoire, et le gouverneur, l'ayant fait flageller, le livra pour qu'il fût crucifié. Les soldats l'emmenèrent et le crucifièrent, et il laissa partir l'esprit.
The cohort and the tribune seized Jesus, bound him and took him to the praetorium, and the governor, having had him flogged, handed him over to be crucified. The soldiers took him away and crucified him, and he let the spirit go.
There is a lot of similarity with the Passion story found in the original layer of the Ascension of Isaiah, once the (interpolated) the pocket gospel is removed:
And again he descended into the firmament where the prince of this world dwells, and he gave the password to those who (were) on the left, and his form (was) like theirs, and they did not praise him there; but in envy they were fighting one another, for there is there a power of evil and envying about trifles. 30And I saw when he descended and made himself like the angels of the air, that he was like one of them. 31And he did not give the password, for they were plundering and doing violence to one another.
[interpolated pocket gospel]
And the god of that world will stretch forth his hand against the Son of God, and he kills him, and he hangs him on a tree, and he kills him not knowing who he is.
«Et princeps mundi illius extendet manum suam in filium dei, et occidet illum, et suspendet illum in ligno, et occidet nesciens qui sit»
[interpolated pocket gospel]
And the god of that world will stretch forth his hand against the Son of God, and he kills him, and he hangs him on a tree, and he kills him not knowing who he is.
«Et princeps mundi illius extendet manum suam in filium dei, et occidet illum, et suspendet illum in ligno, et occidet nesciens qui sit»
In both the cases there is the explicit distinction between the moment of the arrest and the moment of the crucifixion. The version of the Ascension is older than the Earliest Passion story because it talks about a death happened temporally before the crucifixion.
This explains why in the Earliest Passion story the premature death has been replaced by the flagellation: an useful expedient to have a suffering but not yet dead Jesus before the crucifixion.
Another feature of the Earliest Passion story is the absence of the name of the Roman governor who crucified Jesus. Just as in Mark the names of the high priests are absent, so also in the Earliest Passion story the name of the governor is yet absent.
Given that it is the mention of John the Baptist in the incipit to fix Jesus in the History, and given that John the Baptist is absent in the Ascension of Isaiah, then it was only after the introduction of John the Baptist that, by mere collateral effect, a name was given to the Roman governor who crucified Jesus.
The connection John the Baptist/Pilate is implicit in the Recognitions and pseudo-Clementine Homilies, where John the Baptist is associated to Samaritan figures (Dositheus, Simon Magus), and Pilate was infamous as slayer of Samaritans.
The mention of Samaritans in a Gospel or more generally in the Christian tradition means 'sectarian division'. Since also John the Baptist entered in the Gospels as a divisive figure (traces of rivarly are survived in Mark, pace 'Mark' himself), then the connection between John the Baptist and Samaritan figures was 100% expected.
By logical extension, also Pilate was introduced, once the Samaritan allusion was introduced.