Any comment on why the scriptures do not mention the cloth over Jesus’s head/face while still on the cross? Not doubting it, just wondering. Was that a common thing to do? Obviously today that is one of the first things that happens (at least in the TV shows!) is that the face is covered. And if it was a common thing to do - then not really worth mentioning perhaps?
I know the Crucifixion story focus's around Jesus’ words, and the events that point back to O.T. prophecies (they didn't rip his garment, no bones broken, etc.)
I recall the analysis of some medical doctors that studied the image on the shroud. Pretty amazing detail of the muscles, how various things respond to the hanging, the suffocation, the build up of fluids (water and blood), etc.
There are no details about many things in the Bible or the Gospels. The authors did not give a step-by-step procedural that was used in either putting Him on the cross nor did they give one about how they got Him off the cross. It was a very unusual thing for Pontius Pilate to even allow the corpse to be removed. Crucifixion victims were left up, often for weeks as an object lesson to the populace. As it was it likely took sometime for official permission to be granted. Recall that Mary, Jesus mother was there, and those waiting for that permission were likely to cover His head with a modesty cloth to shield her from seeing His dead face. Such a thing was done with normal Jewish deaths. A sweat cloth from one of the men could have been impressed into service and draped over His head. The patterns of stains on the Sudarium of Oviedo suggest thats exactly what was done. It was kept there during the removal and transportation process.
First position: while on the cross.
Second position: while being carried to the tomb Third position: In the tomb, only more tightly rolled, used as a jaw binding, with the knot at the crown of the head. Worn sort of like a toothache wrapping like this:

Except it would have been under the beard and behind Jesus hair, which accounts for the forelocks on the side being pushed so prominently forward.