the only "regulation" for the fuel pump is the MAS relay, which controls the pumps, ac compressor and has other functions. there is no pressure switch to shut off the pumps. the shutoff is because of a timer built into the relay to prime the system. the pumps stop until an ignition signal is received by the relay and then the pumps run again.

you do need to know what the fuel system pressure is when the car doesn't start. needs a special set of gauges to test. i can't relate to WHY the pumps are cycling 3 times and then no start. sound like a relay and/or another problem. keep in mind, you need to know if there is spark when it won't start. the MAS relay has no control over the ignition. good luck, chuck.