I know this forum is a little bit old :), but I think I have to share my experiences with the "JUST CLICK" problem.
The Kawasaki - I don't know why - a little bit complicate the starter circuit.
IGN Swith + --> Stop Swith --> Start Button -->IGN Coils --> Fuel Pump Relay --> Fuel pump --> J.Box diode --> JB starter relay --> Head Light Relay --> and the Last one STARTER RELAY. it is a little funny.....NO NOT FUNNY, because I suck with this problem every day. I change battery, fuelpump relay, starter relay, but didn't help for me.
I love the Kawa ZX7 And I never change with the suzuki! But look at the suzuki circuit.
IGN Swith + --> Stop Swith --> Start Button --> STARTER RELAY. A little bit shorter and when you push the button - Chemical Brothers yeee - the STARTER RELAY get about full battery voltage ~ 12,7V intead of the kawa where the starter relay get only about 6-7V.
Because the IGN coils, Fuel pump relay, fuel pump, diode, etc takes the VOLTAGE from the STARTER RELAY.
The 6-7V is very low, and usually not enough for the STARTER Relay.
So yesterday I killed this problem forever. I have modified the Juction Box. I cut the JB Starter Relay switched point from the 6-7V input. And because I have an unused fuse (ACC fuse) in the JB I liked this output with the JB Starter Relay switched input point.
So now when I pussh the starter button the JB starter relay send ~12V to the STARTER RELAY insted of ~6-7V.
And voila the ZX start every time! ;)
I hope I can help someone who suck this problem in the future.
Circuit diagram modify: https://goo.gl/z3zhdu
JB soldering modify: https://goo.gl/yTsfe7