I finally decided to just trace the whole system out by hand. I'll attach the resulting diagrams in case anyone else needs them -- please excuse my handwriting.
Note that these aren't complete -- there are a few mysteries left:
- Where does the brown wire get power? It seems to get it from the stock HVAC system but I've been unable to figure out where.
- What does the blue wire do? I think it shuts the system down if the ignition is on, so the two compressors can't fight, but I didn't think to test this theory before buttoning everything back up.
The problem with my system turned out to be a single relay -- the one under the dash had a burned out coil, preventing the system from switching from engine mode to external power mode.