My Dometic fridge uses the festoon bulb (that looks sort of like an old fashioned glass fuse) as well.
I'd check drawers etc. for the missing bulb. On my fridge, at least, the bulb circuit is live all the time, regardless of whether or not the fridge is turned on, though I gather this is not universal for all Dometic fridges. (There is, of course, a door switch in the circuit so the light isn't on when the fridge door is closed.) The only way to have the fridge open when shut off (for ventilation, to prevent icky stuff from growing and smelling bad) was to take the bulb out. I added a shut-off switch because I got tired of fiddling with the bulb, in fact.