How do I check to see if my neutral light problem is from the LED unit or the neutral switch?

 

The neutral indicator lights up when the neutral switch allows the circuit to go to ground. HD put a simple connector under the bike (I believe around where the rear brake pedal is on the throttle side...look for a single tan wire and follow it to a plug). Pull on both sides of the plug to disconnect. On the end that runs back to the handlebars...take a small piece of wire with stripped ends. Put one end in the connector going to the handlebars....take the other end and touch a mounting bolt, frame or other known good ground.

With the ignition "on"....doing this your LED should light up. If it does....then the problem is from that connector you pulled apart under the bike to the neutral switch...and most likely the switch. If it doesn't light up....then you have an open condition somewhere before that plug going back to the handlebars.