Throttle Cable Source
 

Where are you able to get the PULL throttle cable for these bikes? I'm only able to find the PUSH throttle cable and now have two of them. Everywhere I have found shows the PULL cable discontinued. Will a cable off of a more modern CBR600 fit?

As long as it has the correct ends and the correct length, yes. On my old CBR I switched to goldwing cables from the same years for the throttle and choke since I had VFR bars on it.