Sorry I was late to the party. Module doesn't run the TBI prime circuit.
Prime is handled by the ECM. It's not every time you turn the key to run, I think it's on a timer.
Check that the wire from the ECM to the relay has voltage when you initially turn key to "run". Not sure what the time is that will allow another prime cycle, but I'd guess 15 seconds or so between the on/off of the key. Since this is a retrofit, I'm going to bet the most common problem, wired incorrectly. Check fuses as well though, if not yet done. I would guess one of the power feeds to the ECM is not getting power as it should (12V run/start), although I'm not certain how power for the relay is handled within the ECM. Could even be the connector is wired incorrectly, if you had to do some re-pinning.
Big cap or small cap, still HEI.