The ground for switched side of relay is what the PCM controls.
If you want to see if you relay works, remove the small wires. Turn key on and test to see which one is hot with key on. Reconnect. Use jumper wire to ground other terminal. The relay will either click on, or not.
On your hydraulic pressure stuff, if it is working but not starting you should here Solinoids clicking. Testing voltages won't give you much info. If you want to know what's up with it install a gauge on a rail. The ipr works off of duty cycle, or percentage of On time. One wire is always hot with key on, other is ground side switched by PCM. If truck is cold PCM can command up to maximum pressure to start (2700ish) So if you were able to watch duty cycle, it will jump up to roughly 30%. A warm engine idling around 500 psi should net a duty of around 11-13%.
But you can either hear or not hear Solinoids. If you do, you know it has hydraulic pressure, if not, then you know it isn't making at least 460 ish. If the PCM doesn't see at least around 450, it won't make everything happen with idm. Mechanically injector needs around 425 to overcome spring pressure internally, but PCM wants to see more. But also, if rail sensor is throwing out a bad reading, who knows. Hence the mechanical gauge.
Your rough running could be an injector, which now has the oil plunger stuck in the drain position, leaving the system not making any pressure at all.