Mine did this too in my 95. I went online and got a replacement momentary switch. It was a pain in the butt after i got it all apart, because switch wasnt exactly right. My suggestion is to have it shipped to rebuild at ford dealership. But for that amount you can have a nice aftermarket CD player which is exactly what i did. But if you like the originality of interior, go for the rebuild from ford.
this happened to Eli's (Mensan)96. I gave him the radio out of my 95 and he replaced the switch. It was still working the last time I was in his car. He is an electrical kinda guy so if you email him he can tell you what exactly you need and maybe where you can find it.