Until I looked up the etymology of chap, I thought this was pretty simple – just chaps, as in cheeks or jaw, as the face, fallen. Like – sad – like crestfallen. But funny because a skull has no chaps, no cheeks and the jaw won’t necessarily be attached.
But it turns out “chap” as a person was already in use in Shakespeare’s time – so he could also be a chap, fallen. Or the sense of cracking open, in fissures, as in chapped lips, a skull might also have a sense of separation – a cracking open between skull and jaw or wear and tear from getting dug up by a gravemaker every so often. Or maybe that’s all a reach and it’s just the jaw.