On a FZS600 is not normal for the fan to come on under normal riding conditions, usually only in slow traffic on a hot day or stood idling for a period. I have a temperature gauge on mine and it very rarely gets above 85C. The fan is only meant to come on round about 100C.
Your problem does seem strange because pulling the plug on the fan switch should break the circuit, so that suggests a short across the plug or the wires to the plug, however if that was the case the fan would come on as soon as the ignition is turned on even with the engine cold. The other thermo switch for the warning light (with a single wire) is on a separate circuit, although still on live when the ignition is on. Sorry I can offer more help, if I think of anything I'll return.