Now this is only coming from years old memory but I believe the brown wire on a kawi usually supplies voltage to the run switch, then out to the coils via the red/white wire. A short to ground in this circuit would certainly affect the ignition. You are already on the right track.
Something hard rubbed through that insulation, obviously metal. A short on this wire would likely kill the bike immediately. This wire supplies all the voltage for the coils, so repair it correctly.
The old kz's have ALWAYS had an issue with voltage drop at the coils. Often a battery that shows 12.8 or better only shows a bit above 10 volts at the coils. Lookup 'Wired George' mod to get improved voltage at the coils safely with the use of a common relay, after it is running again of course.