By your statement it may be the city connection has a bad check valve or debris in it not allowing it to seal causing a loss of pressure telling the pump to run. Also the diaphragm in the water pump could have debris or is faulty not allowing the system to hold pressure as well. If you eliminate these scenarios and the pump still comes on intermittently I strongly suggest that you check for leaks along as much of the water system lines as you can possibly see or get to, many times leaks or seeps don’t show up until your floor has rotted.
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