The headlight relay on a 1996 Ford Thunderbird is in the fuse box on the driver's side of the dash. The fuse box can be accessed by opening the driver's door and removing the small door on the side of the dash. The headlight relay is the same one as for the battery.
The regulator for the 1997 Ford Thunderbird is bolted on the back of the alternator. While the regulator can be changed separately it is more commonly changed along with the alternator.
The relay is located in the engine compartment in a relay box. It is a long narrow black plastic box with removable lid, and sits next to the radiator overflow/fill reservoir. The fuse you are looking for is in location #13FL.