Sounds like you may have a loose connection or pinched wire. Always start with the basics so before tearing anything apart you need to use a voltmeter to test the wiring. You should be able to find a wiring diagram either on this forum or a Google search. It would be best to get a service manual because it will show you how to test each connection as well as the switches. There are some manuals on this forum that you can download so check to see if there is one for your bike.I have a 2000 Honda trx350fm 4x4, neutral light works but comes on in different spots, reverse, neutral and first gear. Sometimes flickers between making it hard to turn on to start. Wondering if or how I can test the shift assembly switch in the rear of the motor before taking it all apart. Now reverse light is eradic ? Seen it can also be the rod that comes from the shift drum! If that's broke motor needs to be tore down. Any help to diagnose before disassembling would be appreciated.
Keep us posted because there are experts here who would be happy to help you with the specific process.