[JRTJH]

The switch for the electric heating element is visible in the first picture. It is directly behind the LP solenoid valve and the "anode rod end" is almost directly in front of the switch. If you look at the "circular gas tube" and put your finger through that circle, you'll be putting your finger on the electric heating element switch. And, if you enlarge the picture, you can see the word "ON" located on the bottom part of the actual switch.

The actual heating element is attached to the dark circular "thing" that is also located in the first picture. It is between the "circular gas tube" and the hole where the anode rod is screwed into the tank.

My "guess" would be that with the tank heating element switch turned off, even if that "not OEM illuminated switch inside" is activated, nothing will happen.

It's "for sure" that the switch inside is NOT factory installed. My guess would be that the previous owner "MIGHT HAVE" (who really knows without asking him) installed a remote water heater switch so he didn't have to go outside to turn off the electric element.

At any rate, the OP's water heater does have an electric element, it is located as described, and the switch is visible in the first picture. Whether it's been burned out by turning on that "extra switch" or not is anybody's guess. I'd start by filling the water heater, turn on the "outside switch" that's behind the gas solenoid, turn on the "inside switch" and see if the water gets got in an hour or so. If it does, then turn the inside switch off, run enough water to cool the tank's contents and wait an hour or so to see if it gets hot again. If it does, that switch isn't for the water heater. But, if the water stays cool, you've found your function. Another way to test it is to get behind the water heater with a voltmeter and have someone turn the inside switch off/on. If you get voltage to that point, you'll know where the wires are connected.

Bottom line, it's a gas (DSI) electric water heater. The switch is behind the solenoid.

ADDED: To answer another question, yes the anode rod is still serviceable. Just use a wire brush to knock off the excess "corrosion" wipe the rod down with some "bleach water", wrap the threads with Teflon tape and reinstall. Tighten enough so it doesn't leak, but don't overtighten so you can still get it out at the end of the season.

All of the comments about the "owner installed switch" controlling the water heater electric element is purely speculation. It may control just about anything ranging from a hidden electric outlet that the previous owner installed under the trailer floor, a "furnace fan switch" so he could filter the air without heat, a second refrigerator switch, fans behind the refrigerator to help cooling, an outside light, or any one of a thousand "what if's" .... But I'd guess it "could be" for the electric water heater element. At least I'd start there.