The WH image shown is only propane fired, 12VDC operated - no 120VAC in that puppy. So typically there is the water heater switch located on the control panel in the RV, the one with the "pilot out" red LED, so if that switch is off, there should be no DC travelling to the WH control plug... the brown or blue wire in the image. A DC voltmeter would confirm that.
If the RV is plugged into shore power, then your lights should not go out. Even with the batteries removed, the converter will supply DC to them, albeit a very rough DC power.
A proper DC schematic of the RV and voltmeter would go a long way in solving this one.
EDIT: The brown wire goes thru the limit switch
before going to the control plug, so my guess is that is the positive DC.
Stay cool
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