The electric switch on that little control panel is only for the propane
side of the HWH. It does not light up at all if you are on shore power electrical
supply,(i.e. using the electrical
element for heating water,) so please don't rely on it as an indicator of power because it doesn't light up on electric.
The light on the little panel only lights
up during the initial ignition cycle (again I mention- only when on propane
,) and then it too goes out after the propane burner ignites. It doesn't stay on all the time. After about 30 seconds it goes out if the propane burner ignites correctly, so you wouldn't even know whether your propane was on or not from looking at the light.
There is an additional "mod" which many of us have done that entails installing a small led light, (this is an additional "owner installed" after-market led, not to be confused with the existing factory-installed one already on the panel,) onto the wiring terminals behind the propane switch. It would allow you to know that your propane is on whenever it is switched on for propane water heating.
In the photo, the extra LED is installed below the existing switch panel, identified by the two skinny black and red wires:
The red wire from the led goes to the red terminal and the black wire from the led goes to the green terminal which will illuminate the led whenever the switch is in the "on" position. If you get a couple of double to single
push on connectors, available at most auto parts stores, you won't have to cut any wires to install it.