Neutral light issues

Been out of town thanks for info, will find a service manual and let you know what I find.

Thanks retro, manual helped me find things. Wiring looks good and connection is really clean. Neutral light still comes on in reverse sometimes or neutral sometimes or first gear sometimes and sometimes it will flash as you go from neutral to first or from neutral to reverse? Like it is moving around a little! If the shaft from the shifting drum was broken I wouldn't think it would be so consistent! I read you can take the swing arm off to get at this! I am not repairing a broken shift drum as I will not take the motor out. So if it is the drum I will wire a neutral delet instead and run it. Any other ideas or thoughts would be appreciated

Thanks for all the help, thought I would post my fix. Seeing how my motor runs good and is not in need of a rebuild I bypassed the gear selector with a toggle switch! Now I can turn the neutral light on to start it up. If or when my motor has bigger issues I will pull it out and fix this at that time.