On my Fridge burner LED I have noticed it is lit when using propane,
switched to 12 volt battery when the engine is running or, when plugged into
110 volt shore power.  Basically anytime the fridge is in cool mode no
matter what the power source.

As a bonus feature....

Sometime when you have nothing better to do.  Turn on the little LED panel
switch when the fridge is not being cooled and the fridge LED light is not
lit.

Now turn on your battery powered faucet.

Cool!  No?

Ron