After all that, I replaced the switch and it started. Came out today and dead as a dodo. Took the airbox out again, and wiggled some wires and it started. I eventually traced it to the LT side of the solenoid coil - white with a red tracer. There was oxidation on the terminal / connector, so I soldered a new connector on the wire, and it started fine. Hopefully it will start ok from now on!