One of the rear lights goes on as soon as the battery is reconnected (I think the outer one), but I disconnected the bulb before doing the testing.
Huh?
This makes no sense and therefore hints at grounds or short or brakelight switch problems. Curious which filament lights up? Brake or lights? That would give you a big clue. How about disconnecting the entire rear wiring harness at the plug up near the left kick panel and re-testing to see if that's where your leak is?
As for testing switches, ohm meter/continuity test while disconnected from the circuit. Make sure that the "off" positions are showing fully open (infinity ohms). Anything lower than infinity ohms while off, is allowing a voltage leak.
Ignition switch could also be suspect and should be tested. Maybe it's actually going into the accessory position instead of the off position. Easy to do on these cars.
