Change a foot valve on a shallow well.
Well pump check valve leaking.
At some point this will reduce the pressure in the pressure switch causing the pump to cycle back on to increase the pressure.
It could be a broken water line from the well to the house usually you ll have a wet area between the well head and the house a bad check valve just above the submersible pump at the bottom of the well a bad connector leaving the well casing or even a broken water line inside the well casing.
If the system was just above the turn on pressure when the water was last used and an ice cube maker ran or toilet leaked a bit the pump would run.
Water pressure is low.
Is the check valve or foot valve leaking.
The house was pre existing but i really question the ability of the pump to hold the pressure in let alone to not have any small leaks in the piping all the way up from the well in the ground.
If the pump motor starts too often that could be indicating something wrong with one of the following pieces of equipment.
This is called intermittent pump cycling.
At water pump short cycling causes we discuss the role of a bad check valve or a hole in the well piping in causing well pump short cycling water and pressure are lost through the leak when the pump runs and air may enter the piping when the pump stops depending on where the leak is located.
The check valve or foot valve is leaking.
Low water pressure can have many causes but most commonly can mean a failing well pump stuck check valve partially closed or bad ball valve or leaking failing pressure tank.
Each of these problems requires a pro.
A leaky foot valve or check valve allows water to drain slowly down the well piping and flow back into the well.
Sand will wear out the pump valves and fill up the bottom of the well.
Check your water supply from the well along with any leaks which could be affecting your pressure cut off.
The water is leaking from the system somewhere.