An alternate view?
Consider how the pressure switch works. It keeps the pump on until the pressure on the output side reaches the set level and then turns the pump off.
We know little about the parts on the trailer group but we have to assume it is much like the motorized where we have super nice detailed drawings of where the lines run so that we can see the route the water uses in the different modes, line pressure or pump pressure.
I feel there are two places which can explain why the pump will shut down as the set pressure is reached but then restart for just a short time later and repeat it all through the night.
But the details may vary for different RV, so it takes a bit of looking or checking to sort which is more likely in any given RV.
The easier one to spot and test is at the connection where the pressure water hose is connected. Looking directly into that connection we often see a small plastic disk which is held against the inside of the fitting by a small spring.
This small disk acts as a check valve to keep the pressure and water from the pump from just blowing out this connection when we have no hose connected and the pump runs!
If you have one of these, it is easy to see what might happen if the little disk is not sealing really well. Depending on line layout, if you push in on the little disk while the pump has pressure built, you will likely get a burst of air and then shortly after a jet of water and your pump will kick on to rebuild the pressure you have released!
If it leaks enough and your pump pushes enough air and water out, you may notice a bit of water in the wet bay, but how close do most of us look if we see water drops in the wet bay? I suspect most would ignore it and figure we dripped some!
A plastic plug screwed into the input port may stop the air leak and be an easy try??
A second and pretty common problem is one I suspect is likely but harder to diagnose and cure. But we do know lots of check valves at the water pump do give people fits when they start to let pressure go back through the pump! It often lets the fresh water tank fill and overflow when we are hooked to pressure water!
If we let the pump build pressure on the output side of the water pump and check valve but that valve lets pressure and water slip back through the check valve, it goes back into the tank and the water pump senses low output and starts to rebuild to the set pressure! No water leaks to spot but the water pump starts at times for no reason we know about!
Just picking numbers out of a hat, say the pump comes on when pressure goes down to 10PSI and runs until it reaches 20PSI on the output side? If that water and pressure leaks from the right side of this drawing back through the check valve at the pump, that 20 PSI it built at the right side is gone and the pump starts again?
Rebuilding the internal check valve in the pump or adding a second check valve in the output line may cure the backflow!