Water Pump loses prime when water tank level is 1/3 full

First, the gauge is not very reliable. Next, the pickup port (a threaded hole) on many trailers is well above the tank bottom, so the pump will suck air at the top edge of that hole. Do what Dutchman said and measure the remaining water, I'll bet it is quite a bit. Now to fix the problem, connect the supply hose to the drain port on the bottom with a tee and plug the original.

I would not count on those sensor readings. Here's what you can try to do.

Use the water in the camper until the pump stops pumping water. Then put a bucket under the fresh tank drain and drain the water, catching in the bucket one at a time and dumping the bucket after each fill. Keep doing this until the tank is truly empty. Multiply the size of the bucket (gallons) by the number of dumps and then you know exactly how much truly remains once the pump starts sucking air.

I think you will probably find, not much. It's actually almost empty. The sensors are miss-reading.

Anyway, if another 15 or 20 gallon is dumped after that, and the pump is sucking air, then perhaps the end of the pipe in the tank is not actually at the bottom. It could have been stuck in too far, its curled upward instead of downward. Or maybe it wasn't stuck in far enough to reach the bottom. Once the tank reached the level of the end of the hose-pipe in the tank, regardless of what's left it will suck only air.

Doing this, at least you'd know for sure how much water is truly left in the tank once the pump quits pumping water. Before fiddling with the pump, I'd then try readjusting the depth of the pipe inside the tank.

You could install a new valve/diaphragm kit for less $$.

Richard