The unit in our hull #12 ran on either propane or electric, as did all the early Olivers I've seen. I don't know if you have the same water heater we had Brandi, but it's likely that you do, but some had Atwood, some suburban, I think.
There's a switch on the outside of the unit to select gas or electric. This was accessed from the outside curbside door. In our old unit, there was also a switch on the face of the curbside dinette, along with a little red light that lit up when the unit first turned on, but did not remain illuminated. It was something I always checked, as I was concerned about accidentally turning on the heater by bumping it, which did happen to us a few times.
There should be a bypass valve under the curbside dinette, so you can make sure the water supply is feeding into the heater. If the handle is turned in line with the pipe feeding the heater, it's open.
Just a thought, before you fill the heater, you might want to check the sacrificial anode and make sure there's still some life in it.
BTW,you are not pestering when you ask questions. We will all be happy to help when we can. I'm just working from memory, as we replaced our original water heater with an instantaneous unit.
And, you're right in assuming that each of the earliest trailers were a little different as Oliver did some tweeks to the design and options. If you can't find manuals online with Google model/make, pm me . I can either scan and send, or send a link.
We all love your little red trailer. Hope you can enjoy (all) of it too.
Sherry