I hope you understand what most folks are saying, l've been in the business a long time and the ON-OFF thing is just silly symantics. Look at your batteries and disconnect switch. If the positive terminal has more than one wire connected to it, the odds are only the largest size wire goes to the disconnect. At the time your coach was built, most inverters were located inside the house and not in an outside storage cabinet. You'll most likely find a device with fairly heavy cables from the battery and then to the 120VAC distribution panel. That should be your converter, use your DMM to check voltage in and voltage out to make sure.
If you don't have a DMM,it would be a good idea to get one. Look up "The 12 volt side or life " . You'll learn a lot there.
If you are experiencing a problem with your batteries draining, you can install a disconnect on the battery side of the inverter.