The voltage to the fuel pump is shut off entirely, not 'drop down', if the engine is not running after 2 second prime. The ECM receives the information of whether the engine is running or not from the crankshaft position sensor. The ECM is basically a computer hard drive that is programmed to collect data from all the various sensors and then sends information out accordingly and gives error codes if something is not within specification. The fuel pump regulator has nothing to do with fuel pump voltage, it is a mechanical device that is not much more than a diaphragm and spring.
If you think you have good connections and grounds, go ahead and install new:
Crankshaft position sensor
Oil pressure switch (redundant fuel pump voltage signal if FP relay goes open)
Fuel pump relay
Have the ECM Reflashed
If you still have your problem after all that, I have no clue, your system must be wired incorrectly
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