It's labeled Atwood EHM6-SM, six gallon, 120v, 1500w, with heat exchanger. There's just the inlet from the water and tank and an outlet split between the bath on one side and the kitchen on the other, so the heat exchanger isn't connected, it currently works only on shore power and is operating 100% electric.
Apparently this water heater has only been made for about 20 years and since the RV is 30 years old, it must have been installed as a replacement at some point. Maybe they didn't connect the switch.
The previous owners seemed really good about saving receipts and manuals for everything from the big stuff down to little things, but there is nothing about the water heater.