Just a thought ....
Shouldn't the pump run continuously? Maybe a power issue with the pump.
Or does the pump have an internal pressure switch so it cycles depending on pressure
IMHO, any oem efi, key in RUN, pump runs for a second or two then off until the engine is turning over. What makes it turn back on can be oil pressure builds over 5psi or so, a vane airflow meter switch, or the ecu based on input from the motor like a crank trigger. This primes the system but the injectors do not open to wet the intake. I don't know how long the sniper keeps the pump on.
On the Sniper, the fuel "prime" setting must be enabled and the amount is adjustable. Key in RUN, after 2.5 seconds, the injectors will wet the intake. I expect the pump is still running at that point in time. It will also adjust the amount based on the coolant temp. Leaving the key on too long without cranking will reprime each time. When the screen has loaded, the pump and injectors are priming.
Some systems also have an inertia switch that the pump control wiring is run through. It is a cup with two contacts in the bowl, a metal ball, and a magnet. A good hit and the ball comes out of the bowl, breaking the connection and shutting off the pump. There is a reset button to put the ball back in the bowl. Most fords have this switch.
I said 58.5 psi before but holley references 58.5 for the regulator, then 60 psi, but say to check that it is between 55 and 60 psi so not critical on this.