The pump does run when the pressure is low. We bought the same pump that came out of the well.
So you have a submersible pump.
1. What is the make and model?
2. How deep is the top of your water in the well?
I should add that the pressure tank is reading 50 psi
Air precharge is measured when the water pressure is near zero. Are you referring to air pressure or are you referring to the water pressure on the water pressure gauge? I think air. 50 PSI is much higher than the usual air precharge. Normal for a submersible pump is to have the air precharge 2 psi less than the cut-in pressure for the pressure switch.
3. What water pressure do you get on the gauge at the tank?
4. How long does it take to get close to that presure?
You could have a water leak, maybe inside the well.
5. When you use no water and shut off power to the pump, what happens to the water pressure?