1991 Isuzu Truck - starts only if you floor it?

Trying to help a neighborhood kid with a 1991 Izuzu truck, 4 cyl. Manual trans, MPFI, tons of miles. It cranks fine, but will only start if you floor the gas pedal while cranking and hold it to the floor while holding key in crank position until engine reaches about 4,000 rpm. (Great for the engine/starter no doubt!) Most times it will run normally (miracle) until next time you need to start it - hot/cold doesn't seem to affect the ritual required.

Both fuel pump fuses are good and the fuel pump relay in engine compartment relay box is good. If I remove the relay and jumper constant battery voltage to the fuel pump, truck starts and runs as normal. My conclusion - relay is getting "crank" voltage" but not "run" voltage until RPM is high enough to trigger the switch-over. I'm guessing it's related to either oil pressure, crank position sensor or alternator output voltage? What should I look for next? Maybe just stop looking and shoot it?