In my opinion, any vinyl top that's peeling should be completely removed. It's inevitable the vinyl top will trap moisture and completely rust out the roof. While that's certainly less likely in Arizona than in New England, it's still a problem.
Getting a new vinyl top for a Mustang II Ghia will likely be a challenge. Almost nobody is looking to restore one of those so nobody sells parts.
remove it, verify good paint underneath. IF you like top, replace after verifying good paint. If paint is not good...or rust...then repairs are needed before fresh paint. If you don't want vinyl, paint it the same color as vinyl and drive on!