I don't know a lot about PATS iv never had to deal with it but from what little I read about it PATS sounds like its just an alarm integrated straight into the ignition working off the ECU... Like I said I don't know much about PATS but some other alarms do have a fuel cut off so that could be. Id take a voltage meteor and check the voltage at the fuel pump wile someone turns the key on and off. Simple if you got good voltage its the pump if you don't it ether PATS or a relay somewhere.
There could be other factors but those are my thoughts on the matter