Get the alternator checked out. If the pump isn't staying on and the GEN light is on, odds are good the alt or the regulator have a problem. The fuel pump relay is supposed to cut power to the pump if the engine isn't spinning the alternator (in case of a crash).
If getting too much voltage or too little you might have issues with spark causing it to run poorly.
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95 Isuzu Trooper Daily Driver
86 Isuzu Trooper reliable backup
77 LUV 2wd stock beltway blaster (resting)
79 4x4 LUV project: 2.6L, 5spd, 31s (eventually)
MEPR: Man, my 4x4 makes all other LUVs look good
