Neutral light does not always go on when out of gear

The neutral safety switch is where the gear selector is on the left side of the transmission go to rockauto.Com and look up your vehicle and the parts to see it

Back-Up Light remains always ON you should check the Park/Neutral Position Switch (A/T) .The park/neutral position switch detects the shift lever position and sends signals to the ECM.
The ECM receives signals (NSW, R, 2 and L) from the park/neutral position switch.

the neutral safety switch is out of adjustment or just bad

if your neutral indicator light stays lit all the time, you have a bad neutral indicator switch or a wiring problem. Look for the neutral indicator switch at the right side of the chrome cover on the transmission. There are two wires that attach to it.

Good Luck
Steve

Did you ever find a solution? I have the same issue.

the red key light is on because of a trouble code, have to get cleared by dealer. neutral light is on because the nuetra switch is bad. need manual with wire schematics to replace if u want to fix yourself.

i dont understand, the bike shouldent start in gear with the lever out it would jump forward when you hit the start button.. there is nothing wrong with the bike by what you say its just a neutral light, witch is a switch find the neutral indicator switch and replace it and your probelms will go away or test the one you have it should test 13ohms in neutral and OL in gear
let me know how you make out