I think I found the problem. It turns out that the DC circuit to the inverter is not shut off by the battery cutoff switch. However, the wire to the inverter had worked loose, and when I reached around to feel the connection, it came off in my hand. Now the battery draw is gone. So I think the loose wire was creating a short and as someone suggested, a breaker was tripping and resetting. I haven’t had time to reconnect it and be sure that it was the loose wire and not the inverter itself. I guess the silver lining is that I now have a rough wiring schematic of the camper for next time.