I'm not that familiar with your particular bike but I do know that in general turn of the century Fuel Injected Kawasaki bikes have no fuel flow monitoring.
In other words if it was a fuel problem there is no way the ECU would know about it and therefore it would not know to turn on the FI light. The Engine Control Unit can however tell if the injectors or coils are malfunctioning.
This doesn't prove that its not a fuel problem but there is most likely something else going on that the ECU is seeing. Being able to get the error codes would be a big help.
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