Sounds like someone has been mucking around with the wiring and you are stuck sorting out their mess. So when the engine is running the alternator should be charging both batteries by energizing the extra isolation solenoid. When it is not running the extra solenoid should disconnect the "truck" circuit from the "house" circuit. That way if the owner runs down the "house" battery they won't be stranded with a run down "truck" battery and a non running vehicle. The alternator, starter, vehicle driving lights, and all the items for the "truck" chassis should be on that circuit. The alternator should be monitoring the voltage for the "truck" battery. Some alternators need a draw to charge. If the alternator does not sense a draw it wont charge at all. Most newer alternators are the one wire alternator type. In this instance you might need a 2 wire alternator to be able to use that second circuit to operate the extra isolation solenoid. I didn't see an output listed but it probably should be 40 to 60 amps at least.
I think you are on the right track but need to talk with the owner about getting his vehicle back to factory specs. It is going to take a little time and money to get the vehicle dependable again.
Please let the forum know what you find.
Art
Last edited by beachbum; 03/04/23 01:05 AM. Reason: added text for clarification