Yes, ^^^
Get/rent a fuel pressure gauge, so you can confirm what you think is happening, is actually happening.
Also, the computer may be shutting off the fuel pumps after engine starts or doesn't turn them on at all after priming.
Computer controls the Fuel Pump Relay, it is located on passenger side inner fender, closer to firewall.
When key is turned on the computer closes this relay for about 2 seconds, priming the system, computer won't close this relay again until engine starts, or you turn off the key and turn it back on.
Computer gets "pulses" from TFI distributor that's how it tells the engine is started.
You can test for this by manually closing the fuel pump relay using a jumper wire.
Look here:
http://www.therangerstation.com/tech_library/OBD_I.shtml
You will see a diagram of the OBD I(VIP) connector, usually located on the drivers side of the engine bay, near firewall, but can be on passenger side.
You will see the Fuel Pump slot IDed in that diagram.
If you put a wire in that slot and Ground the other end the Fuel Pump Relay will close and stay closed as long as the key is on.
If you use the jumper and engine stays running then you have a problem with the computer or a problem with computer "seeing" pulses from distributor, i.e. computer doesn't know the engine is running.
The Fuel pumps run all the time when engine is running, they don't cycle on and off, so you can drive the truck with jumper in place, it is just a safety issue in case of a fender bender, if a fuel line should break, the engine shuts off from lack of fuel so computer would shut off the fuel pumps, with jumper in place the pumps would stay running until key was turned off, so you could end up sitting on a big pool of gasoline.........................never a good place to be
There is an inertia switch in the passenger footwell that cuts fuel pump power in case of an accident or roll over, jumper doesn't effect that safety switch, pumps would be off if that switch is tripped.