One more place to check. With the engine running, check the yellow wire connected to the "Ignition" terminal (BIRD). It should be about the same voltage as the chassis battery. If it is 0V, check the fuse in the front compartment (under the driver's seat).
To check the Trombeta solenoid. Start the engine, the chassis battery should be ~14V. You already measured the coach batteries at 12.59V. Push and hold the "Aux Start" dash switch and recheck the coach batteries. If it is the same as the chassis battery (14V), the solenoid is working.
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