I fixed this identical problem on my '90 Pontiac...Cause: Intermintent open Oil Pressure Switch.....Detail: When the ignition Sw. is turned-on, the fuel pump relay turns on for 2 seconds and pressureizes the fuel system. After 2 sec. the relay opens and the oil pressure energizes the parallel connected oil pressure sw. and turns on the fuel pump.If the fuel pump side of the oil pressure never turns on this sw. the fuel pump will not continue to run and the motor stalls....REMEMBER THE OIL PRESSUE SW. HAS TWO SWITCHES INSIDE, ONE FOR OIL PRESSURE AND ONE FOR FUEL PUMP PWR...THIS IS A SAFETY FEATURE TO PREVENT ENGINE DAMAGE IN THE EVENT OF NO OR LOW OIL PRESSURE...