8 to 10th Century Roman/Armenian Casket Figures

[Flavivs Aetivs]

This makes it problematic in a Roman context, as Romans did not commonly wear hats, and so had no need for a formalised gesture of removing one...

They didn't commonly wear hats until the 3rd century AD. Then the Phrygian cap became popular, and was quickly replaced by the Pileus Pannonicus.