Let'* start this from the beginning. The fuel pump will prime once for 2 seconds when the key is switched to on/engine off. When the key is turned to START, the pump will turn on and stay on until the key is released to the ON position so as long as the engine is running. If the ECU detects the engine is not running, it will run the pump for another 2 seconds and turn off. That is it. The fuel pump will not run constantly if the ignition switch is simply turned to the ON position, or if the engine was already running, the pump will not continue to run once it has stalled or ceased running due to some anomaly.

So, with this information, what are your findings now?