Are you sure it is GEN/COM and not GEN/CON (GENeral and CONverter) ?
That is how I would read it.
Try this.. Turn on 12 volt lights while plugged in, Note how bright they are Note if Fridge is on AC or Gas... plug things into 120v outlets Small fan, Night light/path light. that kind of things will do, you can use most any light or a radio if you like.
Turn it off and see what happens.. I'm guessing fridge will switch to GAS. some lights go off and house lights (12 volt) will dim a bit.
The dimming house lights are the converter shutting off (it outputs 13.6 in float batteries 12.6 if fully charged so you loose a volt)
Take notes, that is what it controls
NOTE: Same procedure for the GFCI chain.