Either will cause your complaint

The diagnosis requires a simple test:

With low fan ON , disconnect the pigtail wires at the sw. If fan still runs , the relay contacts are stuck closed .
If fan stops with disconnect, then sw is suspect [ as long as PSI is below spec cut-on]
BUT ...be aware that cut-in is lower than gauge reading by approx 20PSI b/c gauge reading and sw reading are different b/c of gauge port and sw locations in the system.

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A Dalton