[Richard]

Only thing I can say on the AH, is put a voltmeter on the terminals for heater element. And work from there. You can trouble shoot forever, but if the element is burned out, the effort is wasted. So see if the element is getting power. If it is not, then we can work upstream through the thermostats the AH uses for the electric element, the overtemp thermostat, and back to the relay in the closet.

I don’t reach the same conclusion you do about the batteries being dead while driving. If the batteries were dead enough for the lights to go out, the engine and transmission computers would have shut down.

On some generator sets, the engine will not stay running if the generator head is not outputting power.

I am checking grounds for the dash board systems, Newell was fond of daisy chaining the grounds. It may be as simple as a loose connection.

Just for grins have you put a voltmeter on both your engine and house batteries?