Headscratch, so... I'm hearing as long as the fresh water tanks have water in them, and you turn on the fresh water pump... mine is located right at the sink area... that will fill the hot water heater or at least put water into it?
Almost. Just as you have to open a hot water valve to let the cold water into the hot water tank so it will push hot water out through the faucet, you have to open the hot water valve to let the air out of the hot water tank so it will fill with water. You have to let the air out to get the water in, and once the tank is full of hot water that stream of hot water only comes out of the faucet because fresh (cold) water flooding in through the inlet in the lower part of the hot water tank pushes hot water out the outlet at the top.
In other words something has to go into the tank to get something out.
At the other end of the equation when you run out of fresh water and there is no water to pump into the tank to force the hot water out, that hot water can't get out (and make the tank run dry) unless you replace it with something else. The only way for that to happen is if you open a hot water tap somewhere in the trailer so air can get in and
open a cold water tap that's below the level of the hot water tank so water can get out. When that happens gravity pulls water out the bottom of the tank and air gets sucked in, but you still have to let something in to get something out.
I don't know about everyone else, but if I turn a tap and nothing comes out, I turn the tap off, turn the water pump off, and go out in search of water to refill the fresh tank.
For sake of argument, let's say I did leave the hot water faucet valve open when I ran out of water. In the only faucet/valve in our trailer that's located below
the level of the water heater is the foot-valve that flushes the toilet. The foot valve only stays open when my foot pushes it down for a few moments at a time, nowhere near long enough to drain a six-gallon hot water tank.
Which is why I never worry about our filled water heater running dry.