Pump priming?

[yokimazoku]

I have the HFS4 kit and and today i was idling for awhile then turned the car off then back on and the pump randomly turned on and stayed on. No flow showed up on the gauge and the low level light blinked for a second then went away. I turned the car off and then back on again and it didnt do it again. I also noticed that when i turn the car on the pump turns on for a split second then off. It does the same thing when i am turning the car off also. Is this pump failure? Also if i turn the key just right and hold it there i can get the pump to stay on. But now flow comes out of the nozzle.