On my Dometic fridge, at least, the interior light will operate at any time the door is open, regardless of the fridge state--even if the fridge power switch is off, in fact. I added a second switch so I could leave the door ajar for storage without having the light on constantly (and without having to futz with taking the bulb out).
It doesn't sound like your problem, but one possible cause of failing to operate on gas that is sometimes easy to overlook is the little gas shut-off valve on the burner assembly--it looks like a smallish knurled thumbscrew. If the valve is off, the fridge obviously won't work on gas mode. If it's one that has had recall work done, you have to remove the outer sheet metal burner shield to get at this valve.
