House Batteries not being charged by engine.

I suspect (and after re-reading I think you also mentioned) that the cylindrical item in the lower left is your solenoid for charging your house batteries while driving. Those do go bad pretty regularly (I've changed a few). Good news is they are inexpensive and that looks like a very easy location to swap it out for a new one.

-Chris

Can you crawl underneath and trace any red battery cable running back towards the chassis?

With everything off (no generator or shore power), measure the voltage on your chassis. Then measure your voltage on your house batteries. They (in your case) should be different. Then measure the voltage on some of those wires to the left of your house batteries. and see which ones match your house battery voltage and which match your chassis voltage. This will tell you if you have a chassis fed battery cable back in your house battery location (...a clue at least).

You can also do these measurements/tests with the engine on. Your chassis battery will likely be somewhere between 13.5-14.3v. Then you can probe those battery cable wires near your house batteries and see if you find a matching voltage. At least this way, you will know if you have your chassis 12v cable in the area near your coach batteries. Then you can probably identify the solenoid that is supposed to charge your house batteries while driving.

Good luck!
Chris