I still can't figure this out. Here are the tests that I've done. The relay has four contacts. With the relay removed, two of the terminals are always hot (12v) and the other two go to ground, as confirmed by a continuity test. This remains the case whether the driver's door is open or not.
The dome light will light when activated by any door other than the driver's door. What is odd is that all the other doors have two wires going to the switch, but the driver's door only has one. I even checked to see whether a wire might have broken off at the switch, but no, the terminal has only one wire.