By the chematic below it appears the starter solenoid always has +12 VDC applied and the start switches just complete the circuit by grounding the negative end of the solenoid. Since it works with the local switch it's time to break out the multimeter and jumper wires, start at that remote harness connection and work your way back to the remote switch (es).
This may help as well:
http://gmcws.org/Tech/dsimmons/onan/onan.html
Thor Forums
