I would guess a leaking vacuum breaker? I think they are usually near the water inlet fitting and are a couple of feet above the floor. Or maybe the PEX connection to the exterior water inlet fitting? Your TT has a slide on either side of the fridge - try taking the exterior access panel off and maybe it's hiding in there? I would expect the PEX line to the tank would be a clear run with no fittings. They sure crammed a lot of stuff in the short space between the slides!
I've pulled a fridge out before and it would help to be able build a temporary plywood shelf or cribbing to slide it out onto. You'd want a cap for the propane line too. Not that hard but I wouldn't want to do it while out on a trip. If you're near a Walmart or RV dealer/shop you could get a black tank wand and stick it down the toilet.
Our vacuum breaker is under the kitchen sink and accessible by removing a bank of drawers. I use our in-tank flusher all the time and would hate not being able to use it.