Nikki wont stay running

[Sterling]

Beautiful carb. Same one I have on my Rx-7.

By "priming" I'm assuming you're opening her up and filling the bowls manually.

The first rule in carb troubleshooting is "Follow the Fuel".
Start with the pump. Is it running? Check the fuse. It should kick on for a second when ignition is first engaged, though I'm not first-hand familiar with pre Rx-7 models.

Next up is the filter. I suggest that the filter would rarely be the culprit in a case like this because if the pump is working then you have an actual obstruction in route from the tank to the carb. But if you have large flecks of crap in the filter from inside the tank, it can help in your diagnosis.

Be sure the tank is breathing properly. When a tank becomes vapor-locked the whole fuel system gets screwed up. If you remove the cap and the tank "whooshes" excessively, there's a problem somewhere.

Blow through the return line to the tank by mouth to be sure it's not obstructed.