I snuck out to the garage after doing the dishes last night and messed around with some of the electrics, inspired by the fact that the license plate light actually worked. Within about a half an hour, I pulled both of the taillight buckets, swapped them out for some better examples in my spares, cleaned the wiring contacts, and got them both working. The front running lights are in worse shape. I had to pull the front bumper off to access them, and found that it weighs a metric ton. It’s made out of 1/2″ thick C-channel and I would hate to be the car on the other side of it in an accident. One of the buckets came out easily but the other is held in with a rusted screw which needs to be extracted.
Finally, now that I can open the driver’s door all the way, I hit all of the retaining screws with penetrant, pulled them out, propped the door up, and screwed it in tight. It now closes almost cleanly, but the door striker needs to be taken apart and lubricated.