Not for certain... but the Jewish burial custom was to place a cloth binding under the jaw, behind the ears and up, tied over the crown of the head, to keep the mouth closed in death. The Sudarium(sweat cloth) of Oviedo (named for the Cathedral it's kept in since the sixth Century AD on Oviedo Spain), shows signs of having first covered the head of a man who was crucified, then used to cover his face while being carried in a face down position with a hand over his face (bloody hand print), and then being rolled diagonally like a kerchief into a rope like form that would be long enough to tie around a head to do service in just such a manner "about the head" as described in the Gospel.
Thanks.
That would still be consistent with the shroud and it’s image, it seems to me.