How long since you changed your fuel filter? My '95 would start tapping a bit when I was getting close to a filter change.
For a simple test, while it's running, take a pair of pliers covered with hose or something smooth that won't damage the hose, and squeeze one of the rubber hoses on the filter side of the lift pump and see if the tapping changes. You don't want to clamp it off with vice grips, just squeeze it together and release it. If the tapping changes, you could try replacing the lift pump.
There's an awful lot going on on the left side of the 5.9 that can cause a tapping sound. The lift pump, all the tappets, the injection pump, vacuum pump, they're all on the left side. For the first 3-4 years I had my '95, I took it to anyone that would listen to it chasing what I thought were unusual engine noises. I, too, replaced my lift pump. Knocks, taps, etc. I finally talked to an old timer at Cummins and after listening to it and riding in it, he told me, "Look, these are noisy engines. Quit worrying about the noises and just drive it. If there's actually a problem, she'll let you know pretty quick." As hard as it was, I took his advice and never had a serious problem from a noise I thought was a problem.