CBR600F 1987
Is there a test for the fuel cut relay?, I have a good ground at the green wire at the fuel pump but only .30 volts at the blue/black wire at the fuel pump connector with the key on. I think my next step should be to test the voltage at the fuel pump when I'm cranking it over.

 

Yes. If you apply +12V to the fuel cut relay the other two pins should short (continuity) should happen as long as the power is on the relay.

Check your workshop manual for guidance. I did this on my CBR929 the other day.

 

Bought a new fuel pump and when I plugged it in and cranked the bike over, the bike started, but the fuel pump was making a ticking noise like 2 or 3 seconds apart then it just stopped and the bike wouldn't crank over (start) again. Starter fine, engine turning. Won't turn over. Maybe I got a bad fuel pump?