A few notes I wanted to log onto this thread, so as to consider later.
As noted above the mytheme death by crucifixion on a tree was ancient and familiar to first century writers. Combine that with the Deut/Genesis link. The usage of the paleo Hebrew TAV as a Jewish symbol for 1. Truth 2. sign 3. life or death. Ez 9:4 places a Tav on the foreheads of those to live. and Then consider texts such as : Sybylline oracles 345: And4 one shall come again from heaven, a man Preeminent, whose hands on fruitful tree By far the noblest of the Hebrews stretched, Who at one time did make the sun stand still (Joshua/Jesus) 350 When he spoke with fair word and holy lips, No longer vex thy soul within thy breast By reason of the sword, rich child of God, Flower longed for by him only, goodly light And noble branch, a scion much beloved....
Further, the Mandean (followers of John the Baptist) connection is usually overlooked. The Drabsha. Drabsha - Wikipedia
Rather than be a symbol of crucifixion it represents the 4 directions and the white cloth is the "Light" of God.