420SEL 1990 fuel starving,I think

[just-n-time]

Just recently I have had some trouble with fuel starvation, Or I should say inter mitten hard start, I have run the pumps and put the fuel gages on it and the upper and lower pressures are good, the pressure is steady. Here is exactly what is transpiring, turn the key on and it primes as it should the car starts and dies, then you can hear the pumps prime several times when you re energize the key. It is as though you turned the key on and off several times. this is not constant most times it will fire and go on. but I am afraid my wife may get stuck some place. My thoughts went to the fuel relay then I thought it might be the fuel regulator. Any ideas?