I hate intermittent electrical problems almost as much as I hate P38 BeCM problems.
Wilson-you have had the original pump out and put a new"er" one in with no change, thus leading us (right, or wrong) that it's not the pump. We don't have absolute confirmation of this, but for now, we're gonna go with it.
Similarly, let us assume that we're not having both ignition and fuel supply problems (work with me here). To isolate one component at a time, let's start with the relay as it's pretty much the easiest accessible. Jumper pins seven and nine-should both be white/purple on a '96. This will run the pump and give us presumptive proof of continuous circuitry between the pump and the battery.
Next, let's take our nifty back probes and begin probing the relays terminals with the key on, ensuring that the rest of the circuits controlled by the "multi-function relay unit" are operational (you'd think that the folks who developed this language would be better users of it). If we can prove that the relay is reliably doing its job, we need to start looking at things like the ignition switch, grounds and the various interconnections in the circuit.
It ain't likely to be pretty boys, but hang on, it might be fun!