A passage from Seneca’s Letters, which seems to me to establish the fact that hiding the face, as a sign of shame, was not a classical gesture.

(Translation)

“Players who imitate the effect of various passions, imitate shame in this manner— they hang their heads lower their words, fix their eyes on the ground & keep them lowered, but they are unable to blush—this can neither be prevented, nor done at will” Sen. Ep. 11. 5²

Artifices scenici, qui imitantur affectus—hoc indicio imitantur verecundiam, dejiciunt vultam, verba submittunt, figunt in terram oculos, et deprimunt, ruborem sibi exprimere non possunt;— nec prohibetur hic, nec adducitur.