I'll start by saying I did a search but could not find the same issue posted.

When I shift into 5th gear the neutral light comes on (2002 FLHT). I have tried multiple sensors. All other gears the light does not come on and it works perfect while in Neutral.

Could the shift drum be worn or shifted in the case carsing this? Or does anyone have any ideas.

 

I'm not trying to be a smartass, but google this "harley neutral light comes on when shifting into 5th gear" and you will get a bunch of hits (some right from HDforums) with the same problem you have.

 

I've found Goggle search to work much better than many forums (including this one) built in search engine.

 

Neutral switch.