the LP system on this truck is an impco with mazda M4-121 engine?
fairly basic LP system, if lockoff checks ok the only other problem could be in the vaporizer which you said you had rebuilt?
and then is the mixer diaphragm, check the seat where the metal bullet inside the diaphragm where it fits over the air inlet nozzle inside the mixer. If it is dirty or the bullet button does not seat properly, if spring is damaged, or if vacumm hose is not connected to correct location the engine will not run correctly.
The vacuum hose to the lock-off hooks directly to the base of the mixer housing. Then there is a second vacuum line that goes from another port on the mixer to the vaporizer as a balance line for the outer diaphragm. Then there is a line between the vacuum lock-off and the vaporizer, usually a steel line.

i would pay attention to the mixer though, it sounds like there is a problem inside that which is why it will crank and run for a sec and then shut down.

Also check the engine oil pressure switch, see if there is more than one pressure sensor, if there is make sure it is not leaking, it could be leaking down while running , loosing its pressure so to speak and causing the ignition to shut the engine down. If there is just one sensor then more than likely it is just for the oil pressure light only and would not affect the engine if it fails.

i did not mention it before, but you said something about the 2 lights lighting up on the dash when the engine shuts off? that is normal, those are the ignition light and probably the oil pressure light coming on when the engine stops while the key is still turned on.