FZ6 won't start

[Gnasher]

Literally all I'd do is bridge it for a couple of seconds to see if that gets the starter motor to turn.

Yes, or run a lead from the battery + and earth out the - on the starter.  But you can do it by checking resistance etc look on page 8.15 onward's safer then sort circuiting. 

You mean the kill switch by the throttle?

I've not seen that mentioned anywhere else in my searches, but I can check it, however, as mentioned, as the bike will bump start, I don't think that's the problem.

Electrics on bikes are often linked in ways not detailed in the manual and error codes are notorious, reading them isn't always straight forward.  It's also possible you've got a intermittent crank sensor and/or connection, could be pickup rota, wet/corroded ECU connector or blown ECU, the later two are unlikely as you can bump start.