You don't state whether you have a steel pressure tank or a tank with a bladder in it & the pressure switch is mounted on tee on the inlet side of the tank or attached to the steel tank itself.
If the pressure switch is mounted on the side of the pressure tank, it is possible that directly behind it where it goes into the tank there is a blockage or rust & dirt build up that needs to be dislodged with the aide of a screw driver.
The pressure switch differential (between cut in & cut out is normally 30 psi)
If you have a tank with a bladder within it then, the problem is that there isn't enough air pressure on top of the bladder.
This air pressure needs to be 2psi lower than the pressure switch cut in.
It seems awfully strange that the water pressure on the gauge returns to 50psi after the tap is opened, makes me suspect there is a blockage on the up pipe, which only allows a certain amount of water through or that the non return valve between the pump & the tank is at fault.
If you disconnect the up pipe from the pump, do you get a constant flow of water? If you do then the fault lies somewhere after that point!
You don't state whether your pump is a jet pump with two pipes down the well. One being the drive pipe & the other being the delivery pipe, with an injector down the well & the pump on the surface or whether you have a bore pump, nor do you state the type of water you have whether it's acidic or full of iron -
Not knowing these factors make it hard to determine what might be the problem(s)
But you can email me on pumps4me8@yahoo.com if you wish & I'll gladly try to sort out your problem.
Note; if the pressure switch is mounted on a tee prior to entering the pressure tank, then it's possible that the pressure tank is water logged & needs to be drained completely..... Release the drain tap & let all the water out of the tank & when the pressure drops to zero then open or remove a bung or plug in the side of the tank to allow air to enter, which in turn allows the water in the tank drain out.Once all the water is out then close all the taps & replace any bungs & start the pump with the discharge tap shut. Once the pump is up to pressure & shuts off then open the discharge line to the source & observe to see if the problem persists.
If you have a pressure tank that has a bladder in it then it is possible that the bladder is perished (has hole in it) These bladders aren't designed to act like a balloon expanding with water pressure pushing it upwards in the tank.
They are designed to work against an air pressure above them! But if the owners forget to regularly check the air pressure then the air pressure can often get depleted & the pump forces the water into the chamber & forcing the bladder upwards like a balloon which it wasn't intended to do!! This is I think might be your problem, co's water pressure is trapped behind the bladder & this would cause your pressure gauge to immediately go back up-to 50psi
Cheers!!