I think you have your switches confused. The white switch on the dash is the one that manually controls the solenoid under the coolant overflow bottle. That solenoid also acts as the battery isolator so when you start the coach the alternator can charge the house battery. This charging circuit however does not go through battery cutoff switch by the door. So if you have the battery switch off and start the coach it sends 12V power back to the 12V electrical distribution panel and that is how Rein's lights were lighting up (when he had the 12V battery disconnect switch open). All you have to do is turn off your battery switch start the engine and check for 12V at the 12V power distribution panel. You will have voltage.... Then if you want to go one step further, disconnect the yellow wire with the red stripe from the solenoid under the coolant overflow bottle and try it again.... No voltage at the 12V power distribution panel. You are correct that the propane/CO2 sensor gets power from the 12V power distribution panel on newer coaches, like my 2017, it actually has a 3 amp fuse.
Nope... Didn't say anything about the switch on the dash by the steering wheel. That is only of value when the engine battery is too discharged to crank the engine. If that switch is "activated" a 5amp line from the coach batteries to the engine battery is connected thus "trickle charging" the engine battery. While that dash switch, I believe, is still installed in newer coaches, PC started putting in Trik-l-Start into all PC's starting in 2017 I believe which eliminates the need for the white switch on the dash by the steering wheel.
That solenoid under the overflow tank in the engine compartment functions simply as a battery isolator... Open when the engine is off or in accessories position and closed when the engine is running. Yes, the Trik-l-Start "bypasses" it when needed based on coach battery and engine battery voltages.
I tried that white switch once when I was parked for 2 weeks in my son's driveway in Canada and due to my own fault, I had left a small 75 watt inverter plugged in the whole time! Almost totally drained the engine battery. I activated that white switch (I was plugged into shore power the whole time) and waited 1/2 an hour and tried to start the engine... Nada! And the 5amp fuse blew. Had to use a real 15a car battery charger fo overnight to get the engine started. Last time I ever tried that switch. Bought the Trik-l-Start after that.
Also, in that line from the solenoid to the 12v distribution panel, there is a 40a self resetting circuit breaker that can just plain quit every few years. They're cheap and easy to replace and the only way you'll know it's dead is if your coach batteries don't charge while driving. I check that by leaving the inverter on. If, after a hour or so worth of driving isn't over 12.8v, that circuit breaker is DOA. I carry a spare.
And just as respectfully submitted,