With a multimeter you can test for yourself if the chassis and house batteries are both charged on shore power. With everything off, take volt readings at the batteries. Then plug in the shore cord and repeat taking readings. You should see a voltage increase on charging batteries. If you want further education, unplug the shore cord and start the engine, then take a third set of volt readings to determine if your alternator is charging the house batteries while driving. Be aware there might be a delay in connecting, so wait 5-10 minutes after starting the engine to get accurate data.
As to the overhead light, turn it on, then turn off your house battery disconnect switch. If the light doesn't go out, you'll know the light is powered by the chassis battery.
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Bob & Donna
'98 Gulf Stream Sun Voyager DP being pushed by a '00 Beetle TDI
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