FYI, it's a Scold's Bridle, not a "skull bridle." Behind the mouth of the mask it has a spiked clamp that is put on the person's tongue. It's painful and prevents them from speaking--hence the name; the bridle was mainly used on women so I found it odd that apparently Pazzi's male ancestor wore it.
https://en.wikipedia.org/wiki/Scold%27s_bridle