No problem other than it does slow getting the right answers! We're good on that..
So with looking at the drawings , I think I can see the most likely problem and it is an area that does give trouble at times. Plastic parts that can get brittle as they get older?
This is what should happen when you are using the pump and water from the tank. A line comes to the water pump and there is a check valve (one way valve?) that lets water pass through to the rest of the lines in the RV as the green line. There is a second small spring type check valve at the water hose connection. You may see it if you look directly in the hole? It keeps water from going out when no hose connected.
When things are right and we turn off the pump and want to use pressure water, it should go in, fill the pipe to the pump and that check valve but the check valve keeps it from going that direction, so it goes up and in the RV.
But if the water pump check valve fails and doesn't close, the water comes in but rather than going UP, it is easier for it to stay low and go through the pump (backwards?) and start to fill the tank!
That's what I see and "think" is wrong but it all needs checking. I think a lot of things that need testing before I believe them!
So some questions?
When you are connected to pressure, can you hear or feel water running in the hose when all the faucets are closed? If so and it's not coming up at the faucets or leaking out on the ground or floors, it's going into the tank!
If you can't tell if water is running, a way to test is to drain the tank first, leave the drain valve open and THEN turn on the hose to see if water starts coming out the drain again.
If this turns out to be true, the fix may not be tooo hard or expensive as parts are pretty cheap and can be found online.
The drawings show it as a Shurflow pump, but pumps are prone to getting changed over the years, so do look at the label on the pump you have and match parts for what you have, not what the drawings from 25 years back show!
Trust what you find, not what I say!!
On the fix, either replace the pump or cheaper and not hard is to replace just the rubber/plastic parts like the check valve. Personal choice and depends on how you want to work it, but I might replace ALL the rubber parts while I had it out as they do get funky if they are the 25 year old parts! I try not to do that sort of thing too often if it only saves a few dollars??
None of the rebuild is tricky or hard but there are often videos online of folks doing whatever brand and model of pump you find.
New pumps can be a good option, too and about all you need to match is the same size hose connections and the gallons per minutes rating. The check valve is built as part of the pump.
Hope that fits and gets you going again!