I've attached a photo of the water tank and the plumbing from the tank to the pump from before. The hose coming out of the bottom (on the right) has a multi-turn shut off, then a tee with another shut off going to the hose used to winterize and the straight run from the tee goes into the bottom of the pump.
I removed the fitting at the bottom of the tank and replaced it with a new fitting, a new short piece of pex into a ballcock into the hose to the water pump, eliminating the tee and the winterization hose, as a test. (2nd photo)
When I started filling the tank, I turned on the bathroom faucet (the highest in the RV) and the pump started right up and shut right off again. Great.
I then turned on the kitchen faucet and it had no pressure and took a long time for the pump to kick on, then to shut off again, just like before.
I mentally gave up and just filled the tank, since it's snowing, getting dark, and I have no more energy for this today.
There is no hose in the tank, and I've replaced everything from the outlet to the pump. Well, I kept the white hose from the ballcock to the pump, so I guess it could be that. I can replace it easily enough since it's after the ballcock, and I may try that tomorrow. I don't think I can connect the pump filter to pex, so I'd have to replace it with new vinyl hose. I purchased a camco water hose (on clearance at Lowes) while buying new fittings, to cut into lengths to do this replacement.
If that doesn't do it, I'm literally out of ideas, as everything from the tank to the pump will be brand new, and doesn't appear to be leaking.
It feels like it shouldn't be this hard, but that which doesn't kill you makes you stronger; I guess
