Thanks to everyone for the helpful suggestions! I did some more testing with my multimeter and found the problem area. At the pump, I checked to see that the input wires from the driver door, passenger door, and trunk were getting 12V in the lock and unlock position. What a surprise, there was 0V from the drivers door. Upon closer inspection, I found that just a couple inches down from that connector, someone had spliced in extra wiring, I assume for an aftermarket remote locking system. I ripped out that wire and soldered it back up properly, and voila, everything works. Odd that it would randomly ground out like that, but whatever.