The Bird senses a 'charge' condition and turns on the circuit to energize the solenoid. If one set of batteries has a significantly higher voltage than the other, that might cause the condition. You have 12 volts on both sides of the aux switch because the Bird is energizing the solenoid. The converter can only charge when you are hooked to shore power or generator. I had the same problem, but mine was caused by me installing lithium batteries, which have significantly higher resting voltage than the chassis battery, which caused the solenoid to energize constantly.
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