What documentary evidence is there that Roman crucifixion victims were completely nude?

Ancient sources are pretty vague about crucifixion. My understanding is that the naked element comes from two sources: a single sentence in the Oneirocritica and from ancient Jewish practice/law. In the Oneirocritica the reference is to "naked (gumnos) flesh" on the pole (stauron). However, this work is about dreams and the context is pretty philosophical, so I definitely would not consider it purely literally. In ancient Jewish practice of execution the condemned was always stoned naked, and this was explicit.

In general, I think you are safe in assuming crucifixions were done naked because ancient Roman slaves did not wear undergarments. Most slaves just had a tunic and that was it. Most did not even have shoes. Take the tunic off and the guy is buck naked. Ancients did not, as far as I know, wear "loin cloths".

Most lower class Romans and slaves wore only a knee length tunic, if they even had that much clothing. Many in modern times have indicated that wearing an undergarment was considered being naked, yet the Greek word that was usually used in the period to refer to someone who was naked was gymnos, which means a complete lack of clothing. Those who try to say otherwise often do so because the idea of public nudity makes them uncomfortable, so they use modern cultural mores to influence one's interpretation of history. Historical studies of the culture of the time indicate that public nudity was not at all unusual for fishermen, or for those working in the fields or in mines, even in cases when there were women present. Nudity in public was also not uncommon during athletic events. The author of the book of Hebrews makes reference to this in Hebrews 12 verse 1, in which he uses the analogy of a runner laying aside the garments and running naked to represent stripping off sin that weighs down the Christian. This is not an analogy that many people in modern Christianity are comfortable with, but the early Christians would have understood the analogy just fine.

I have seen many insist that the Romans couldn't have crucified people naked or that Peter couldn't have been naked on his boat because they "can't imagine" complete nudity in front of passers-by including women and children could have been acceptable. I would say that how we imagine the past to be does not determine that is how it was. Nudity has been used in punishment throughout history, and has also been common for those working in physical and dirty jobs (fishermen, miners, etc.). Defeated people throughout history had their clothing taken away to shame them. This shame was not the shame we have in modern times due to the mores that originated in the Victorian era, it was because to be denied clothing was the mark of a slave, though the same people who would have been shamed by having their clothing forcibly taken would willingly lay it aside to work or exercise if it was their choice. The shame, then, was due to forced nudity, not the state of nudity in and of itself. A modern analogy might be that a person would likely feel embarrassed and shamed if they were attacked and had their clothing stripped off of them leaving them in just their underwear, yet when they go to the beach they might be perfectly willing to wear a bathing suit that covers no more than the underwear would.

The problem with many people today is that things like this in history don't make them feel all warm and fuzzy and so they dismiss it due to their FEELINGS. Well, feelings don't define the historical record, and if someone thinks they do they are dabbling in the wrong field.