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Carlton, good point on the wts light. If you monitor battery voltage during the GPR on time, the voltage is certainly a good enough indicator of when the relay times out. In the cold weather I sometimes look at the trailer brake controller (which shows battery voltage) to tell me when the GPR cycles off.
I also would like to bring up the -------! grounds. There can be many different results from bad grounds, especially the ones adjacent to the PCM. Corrosion under the hood at the ground locations because no engineers at any truck mfg. plant thinks these trucks will be run on salty roads. A little light grease, or antioxidant grease, or whatever, even light axle grease would totally prevent many of the corrosion issues. That said, for some reason I don't think grounds are the issue here. But who knows? This is definitely a weird one. Larry
Having had similar issues as you described, I finally determined that my battery terminals and wires were corroded. Replaced the terminals and thoroughly cleaned all the wires and, viola! Seems that the batteries can have plenty of voltage to crank the engine, but resistance in the bad connections reduces voltage enough to cause the injectors not to fire. The connections didn't really look "bad" and the batteries were new, which kept me looking elsewhere. What you describe sounds like the batteries losing just enough voltage after the glow plugs kick on for awhile to not fire the injectors. Worth ten minutes to pull and clean all the battery connections, free and they probably could use it anyway.
Good call on the battery cables, Mr Schulz! Even one bad battery out of two can also cause weird problems. The switching power supplies as they are known can be very sensitive to power supply voltage fluctuations. The IDM module for the injectors is fairly power hungry. The changes in voltage can get past the power supply and confuse computerized modules or the power supply does not work properly when the voltage is varying.