I have replaced my alternator,idler pully, and belt. All parts are ford parts and # match according to vin. The battery is charged at 12.82, and the gauge in car reads above center. Why is the battery light on?
Not sure. Have you tried replacing the battery? 12.82 sounds a little low to me, but I might not be remembering what it's supposed be. I'd try borrowing a battery and seeing if that fixes it.
Your alternator is not charging, you said you have already replaced it so it has to be an wiring problem.
Check to see if you have 12v to the alternator on the large (BK/OG) colored wire at the terminal on the alternator. Also check to see if you have 12v at the alternator connector pin A on the (YE/WH) wire.
I had a '99 GT that did the same thing, it flickered on and off randomly for a year, never had any voltage problems and the local shop had no idea (big surprise). Guess this isn't much help, just lets you know its prob a stupid sensor problem and you're not alone