I'm thinking one of my first guesses was correct, FPR.
I was fiddling around with it tonight, put a new fuel pump relay in, no change and I can hear the in line pump running all the time with the key on.
Then my buddy comes over and pinches my return line while I start it, boom, stays running as long as I want it. As soon as I remove the vice gripes, it slowly dies.
Parting Out Complete 96 328is