Sounds like a fuel supply problem (acceleration increases demand). Truck of that age I'd be looking at all the fuel suction lines for soft or collapsing hoses or air leaks. A older style Cummins fuel system like this will tolerate a bit of air in the fuel but will usually stumble on acceleration.
Based on what you said...an overhead adjustment (valves and injectors) isn't causing this....but on an N14 you should be doing this every 200,000 miles or less. They were a bit finicky if things got out of whack and could prematurely lose an injector. And when you do get this adjustment done ....spend the money and get a real Cummins shop to do it. There is a quick way....and a right way...and when it's done right you won't believe how smooth the old iron can run. Also, the quick way...if the adjustments haven't been done for a while...will bind up the injector plunger resulting in you needing a new injector for each one that binds up....saving a hundred can cost a thousand kind of thing.
