No, Darnit, The Light Doesn't Go Out When I Close The Door!

DrewE wrote:
Some RV fridges have a switch of some sort that turns the light on all the time, using it as a little heater (for climate control or cold weather operation or some such, I can't recall precisely what at the moment).

Never heard of anything like this nor would it make any sense at all. Yes, gas absorption fridges usually have a climate control heating element wrapped around the perimeter of the freezer door to help minimize frost build up. It's a 12 vdc heating element so when dry camping it's drawing down the battery, however manufacturers in recent years started deleting the switch used to turn this element on/off. This is irrelevant if you're camping on an electric site but if you're dry camping it's unnecessarily depleting the battery. The solution is to add your own switch, just as I've done ... however, this has nothing to do with the fact the fridge light is not being turned off when the fridge door is closed. In the OP's case it sounds like the switch is faulty, if so just replace it.