A loss of fuel pressure or erratic fuel pressure delivery when you hook up a pressure gauge , a drop in volume/out put or an erratic oscilloscope pattern. Another test is if the engine stops running get a friend to crank over the car, kick the fuel tank if the engine starts you have probably jarred the fuel pump back into a working condition but its failure is immanent.
One sigh is a drop in fuel mileage and or loss in power. The model of Cummins you have the lift pumps go out every few years depending on what they are replaced with. If it is an injector pump you could have many issues but they will be more serious, missing at idle and very very poor performance.