Have you check the city water connection......is it dripping?
They have a check valve that can leak so pump would cycle.
If pump is running continuously then it is either not building up enough pressure to trigger pressure switch, pressure switch is sticking or pump discharge pressure may need to be adjusted.
On the end of pump head is an adjustment screw.
Turn it clockwise 1/2 turn at a time (1 1/2 turns MAX) to increase discharge pressure. Pump should build up pressure/shut-off (with no demand) within a couple of seconds (after lines have been purged of air cold/hot sides)
With a faucet wide open pump should run then shut off within seconds after closing faucet.
IF no leaks (low point drains, showers--inside/outside, city water connection, fittings etc.) pump should only run under demand.
IF adjustment doesn't work and no leaks....pump pressure switch or pump bad.