Jim, You have lots of good advice... the neutral switch is just an idiot light tied to the shift drum where there is a long peg that closes the circuit when the bike is in nuetral. This peg is at the 8 oclock position when properly oriented and if the light works SOMETIMES but not OTHER TIMES, then there is just a bad contact which isn't unusual. The pin touches a depression in a little plate which is fastened to the end of the shift drum by a 5mm bolt or screw. In any case, it has zip to do with the starting issue.
You most likely have a clutch interlock. The way your start system works is that voltage goes from your battery to your starter via a relay (solenoid). When the solenoid is triggered by a voltage, the thing closes internally, and power goes from the battery to the starter. The trigger power comes from a fused circuit that first goes through your ignition switch, then the kill switch and then to a button in the right switch gear. The interlock part where the clutch must be squeezed is powered by a wire coming off the kill switch and then going to the start button instead of directly wired inside the right switchgear.
To troubleshoot this system, first check your NEGATIVE battery cable and ensure it is securely grounded. This is the most likely cause of a no-power type situation. Ensure both cables at both ends are cleaned and coated with dielectric grease to prevent corrosion.
Second test is to take a heavy gauge wire and touch the POS battery cable and the lug on the starter relay (solenoid) that has the cable connected to the starter... it is fat and black... about a 10 ga wire stranded copper cable I would guess. If the starter kicks over, the starter is likely OK and if not, you have a starter or starter clutch issue.
Next, you need to test the relay. Take a smaller gauge wire and touch the POS battery cable with one end the other end touch to the soldered-on small gauge black wire connection... this wire is either 16 or 18 gauge I guess, that is soldered onto the solenoid side between the two big lugs where the battery and starter cables are connected. This connection is the "trigger" that comes from your starter button. If you have the relay click and the starter spin, the solenoid is good.
OK, at this point, if you are still having issues, the problem will be in the the wiring that leads to the starter button or in the clutch interlock switch, ignition switch or kill switch or one of the associated connectors. A test light is handy so you can quickly look for the point where the failure is occuring.
OK... wire going to ignition switch... there is a major connector going to the ignition switch, separate the connector and clean/dab pins with dielectic grease. If you have a bad connection here, it will be on a FAT white wire coming from the harness which is the main lead from the main fuse. This wire should be HOT all the time. Check it with the light by grounding the light and touching the probe part to the white wire. I am pretty sure it will come on if anything else works when you turn on the key. If it doesn't, the problem is fuse or fuse block related since there is a wire going direct from the battery to the main fuse.
Next, when you find power, reconnect the ignition switch. Look for the wire coming out of the ignition switch that connects to your kill switch. You can look up the wire color yourself but the only point of failure here will be the ignition switch or connector between the ignition and kill switch. Open this connector, clean with electrical contact cleaner and dab pins with dielectric grease. Now, turn on the key to run position and check for voltage on the pin associated with the wire that goes to the kill switch. If there is NO POWER, the ignition switch is bad. If there IS power, connect the connector back up and move on.
Now, if there was power, you need to check the KILL SWITCH. Open up the right switchgear and look inside. Note there is a black wire coming out and going back out of the kill switch. The kill switch is a VERY LIKELY source of your problem. Turn the key on again and check for power using the test light on the wire coming directly out of the switch... put the probe on the exposed part of the wire inside the switch gear. If you get the light to come on with the switch in the RUN POSITION, the switch is OK... if not, jiggle the switch. If you find the power comes on, even sporadically, the switch will need to be fixed to where it will work properly, or replace the switch, or bypass the switch. I would recommend the first two options rather than bypassing the switch.
OK... you found power with the switch in the run position... Now you have a black wire going over to the clutch perch where there is a switch. This switch must close in order complete the loop back to the ignition switch that the power takes to trigger the solenoid.
Test the switch by turning the key on, put the kill switch in RUN and check for power where the black wire comes back into the right switchgear at the start button. If the light comes on WITH THE CLUTCH PULLED IN, the switch is good... if the light doesn't come on, the switch is probably bad.
You can further test the switch by taking loose the wire that goes TO the switch and the wire that comes off the switch and put a piece of wire in both connectors which effectively bypasses this switch. Turn the key on, put the kill switch in RUN and check for power where the black wire comes back into the right switchgear at the start button. If the light comes on WITH the power to/from the switch jumped, the switch is likely bad.
If you find the switch good, last thing to check is the start button and connector to the main harness where it connects to the solenoid. You have power TO the button... OK, put your probe on the wire coming off the start button... it is a black wire. You can pull open the right hand switchgear connector (that connects to the main harness and check for voltage here using the light touched to the black wire associated pin. Use some spray electric contact cleaner and dielectric grease on the pins. Turn the key on, kill switch on, pull in the clutch lever after re-hooking the wires properly and push the start button (it is good to have a couple extra hands for much of these tests). You should see power by the test light lighting when you push the start button. If you don't, you can try cleaning the contacts by light using some steel wool and slightly stretch the spring behind the button to tension it but if you still can't get it to work, then replace the button.
The only other issue you might be having is that the main wiring harness has been opened up in the past and the wire associated with this circuit has been cut and spliced back together and there is a bad splice.
Geesh... I have typed enough for today.