Sounds like fuel delivery...
Make sure you dont have air escaping into the fuel line. Theres a rubber connection that jumps the steel line coming fromo the fuel tank to the steel line going into the lift pump. Its on the frame rail in front of the rear passenger wheel. Make sure this hasnt deteriorated and that the connection is still good.
Check the bleeder screw on top of the fuel filter housing that it hasnt come loose. Make sure the filter base is tight as well.
Whens the last time you changed the fuel filter? If the 'Water in Fuel ' light has come on in the past few hundred miles you may need to replace it anyway. BTW, the WIF light will activated if there is a restriction in the fuel line. Something to keep in mind...
Lets check to see if the return line injector is clogged. This is the injector on top of the injector pump that faces the front of the truck. It has a 'J' shaped rubber hose that runs from the RL injector down to a hardline that runs into the motor's injectors. Remove the rubber hose from the injector and get a deep socket (9/16 I think) and take it off of the IP. Look insiide and see if theres any debris. Inside this injector (reminds me of a spark plug) is a clear glass plunger that acts as a one way valve. It should be clear and move freely. If theres crap inside /it doesnt move freely back and forth get an allen and some carb spray and clean it out until it does.
If these things dont solve your problems then you may have a sick lift pump. Its found on the front of the motor, passenger side, kinda low. Should have 2 steel line going in and out of it. It helps to pull fuel out of the tank and up to the IP. You can use the civy 6.2 version found at any zone/pep/napa store. Tell them its for a 6.2 diesel, though it may resemble a mechanical fuel pump for a chev350. Its a "J Code" motor BTW, if the counter guy asks, not that its a big deal. Buy some 'line wrenches' if youre going to change the lift pump, the steel ines dont want to give easily after 25 yrs and they come in handy for other projects.
Let us know if this cures your problem or if you find something different. If you follow this I think it will solve your problem though. These are the most common hassels we've all dealt with