Weird Mustang Rearview Mirror Problem

I just bought my son a 1999 Mustang convertible to replace his 1995 that blew the tranny. The car has a strange problem in that the lights on the rearview mirror stay lit continuously even if you turn the switches off. I have unplugged the power to the mirror as a result.

I thought it would be a bad switch at the doorway; however, I think the problem is actually in the mirror. Any ideas? I'm thinking about just replacing the mirror assembly. Would one from a 1998 fit a 1999? ~Gene