covers on the headlights of my 1987 Le Baron

As I recall, there's a relay block under the driver's side of the dash, but it's a sealed unit. Those that I've run into before acted like there was a broken solder connection on a relay, which is pretty common on many applications. If your assembly is sealed and you can't find a replacement, the guys at a tv repair shop may be able to peel it apart to look for bad connections.

If you find individual relays plugged into a box, swap the relays around to see if a different function stops working. Those relays should be fairly standard and you should be able to find plenty of replacements in a salvage yard.