The relay can die, it is under the cover on the passenger side fender. The other thing that can cause problems with the fuel pump is the alternator or voltage regulator though. The pump is designed to only run when cranking the starter or when the motor is spinning.
I don't recommend bypassing the fuel pump relay without at least some safety cut off, it could be the only thing that keeps from causing a massive fire in a crash. Somewhere around here a while back someone figured out how to wire a bosch type relay into the harness in place of the fuel pump relay.
If the truck fires for a while when starting then cuts out when the key is turned back from start to run also check the ballast resistor on the coil.
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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