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If the pump is short cycling then the likely culprit is the holding tank not the pressure switch. When the diaphragm in the tank fails (assuming you don't have an old galvanized tank) there is no pressure cushion so the pump short cycles. This can also happen when the pressure in the diaphragm is set too low.
With no pressure on the water piping (gauge at 0) you set the tank pressure at 2 psi below the cut in pressure of the switch. So if your new switch is a 40/60 switch you set it to 38, a 20/40 switch would be 18, etc.