Welcome, Nate. Glad to hear you are bringing a '90 ZR-1 back to life.
I'm afraid it's been too long since I've worked on my fuel pump to remember the details about that system. I think the FSM has troubleshooting steps to help you identify the problem(s). Marc Haibeck might be a good person to hook up with. He may even have something on his web site regarding the fuel system. It's worth your time to look at all of the technical information he has provided:
http://www.zr1specialist.com