Sounds possible, but I'll bet my 10 bucks that it's the multi pin connector on the right side of the cab ( from the oustide, it's just in front of the cylinder. This is where the wiring harness you were tracing eventually leads). Undo the connector and hit it with compressed air and CRC - this has solved many random electric control problems on 9X00's. Then again, I've been wrong before....
Can't help with the A/C problem - good luck.
Can't help with the A/C problem - good luck.