Two thoughts, one that sounds kind of too far out is the wiring may be intermitant and tricking you?
But then a second idea is that the pressure sensing that tell the pump to turn on to rebuild the set pressure may bea sticking?
Are you familiar with the pressure adjustments on many of the RV pumps?
I see in your profile you show a 26 foot? Perhaps a 26A?
Taking a look at the parts drawings here:
https://catalog3d.winnebagoind.com/menu/Parts.htm
Click this snip for best view or go direct for the big picture!
It looks like th epump is mounted vertical with the adjustment pointed down??
That may mean you can't spot the screw adjustment without taking the pump loose? But if you can get to the small screw, leave the pump connected and turned on, you may be able to turn this screw just a 1/8-1/4 turn to change the setting and it may give you some relief?
Cheap try if you can get to it but the other idea might be that you have to put a new kit of parts on the pump for the adjustment. It sounds like something in that pressure switch is sticking!
I like the cheaper/easier if it gets me what I need. I buy the whole pump only if I have to do the radical stuff!
If needed the model of pump and a search will likely turn up rebuild kits and they are easy enough for many to dIY the replacement!
Best of luck to you !