I would think that it's more likely an injector than the pump. You could find which cylinder it is (either by listening or cracking the lines open) and pull that injector..... maybe swap it with one that works and see if the problem moves to that cylinder. Or just have them all rebuilt.

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1985 300D Turbo ~225k
2000 F350 (Powerstroke) 4X4, SWB, CC, SRW, 6spd ~148k
1999 International 4900, DT466e (250hp/660 ft/lbs), Allison MD3060 ~73k