Get a copy of the Haynes Manual or search for a copy of the FZ6 Service Manual and look for details of how to put the bike in Diag (nostic) mode.
Diag 1 shows the output of the Throttle Position Sensor. It should scroll smoothly from (IIRC) around 17-18 to 99-100 as you open and close the throttle.
If it doesn't, it should be replaced. There was a recall on them many years ago, but you may not be able to get that done now.
Whilst you're at it, I'd suggest stripping down the right hand switch gear and throttle and checking the cables and action, then clean everything up if there's rust and apply lube into the cable tubes if needed. Also check the throttle freeplay is in tolerance.
After that, look at the cable connection at the engine end and see if they move smoothly.