What is a neutral switch you say? The Neutral Switch is a safety feature that, when working correctly, will not allow the Starter to engage while the bike is in gear.
As shown in the following diagram, the starter relay, or solenoid, has a positive potential applied when the ignition switch is on and the start switch is depressed. But on the negative side, in order to get back to ground and the negative side of the battery, either the neutral switch or the clutch switch must be engaged.
Tapped off the neutral switch is the wire that supplies the ground to the neutral light. The neutral diode is placed between the neutral switch and clutch switch (and the starter relay). As a diode will only pass electrical current in one direction, this allows either the neutral switch or the clutch switch to apply “ground” to the starter relay. However, when the clutch switch is activated, and the neutral switch is not, the current will not go through the diode and apply the ground to the neutral light. Therefore if your neutral light “lights” when you pull in the clutch, the diode is shorted and needs replaced.
When the neutral light stays on when in gear, but not as bright as when in neutral there is a resistance in the neutral switch that is reducing, but not eliminating, the voltage (ground) being applied to the neutral light. This reduced potential is also applied to the solenoid and is not a good thing.
The neutral switch sits in the lower part of the engine block, and the gunk and carbon gets built up on its contacts over time. This creates an alternate path for voltage through the switch. This alternate path is not a “direct short” and has some resistance to the current being drawn by the neutral light. Resistance whether from corrosion or carbon buildup will be dissipated as heat and drop some of the voltage being applied, hence the dimmer indicator light. If the resistance gets low enough, the safety factor of the neutral switch will be defeated, allowing the starter to operate with the bike in gear.
My advice to anyone with this problem is to bite the bullet and fix it. New switches are available, as of this writing, and replacing a switch with a used switch (been there, done that) is not justified as this task is enough of a PITA to not want to do it over. While easier to replace with the engine removed, it is not impossible to do in the frame. The procedure is in the Honda Service Manual and a walk thru here.
http://www.ngwclub.com/forum/viewtopic.php?t=14520
That being said, you have several alternate options (not recommended but here anyway.)
- Ignore it.
- Black tape over your neutral light.
- Disconnect and insulate wire going to neutral switch (will require pulling in the clutch to start the bike, and the clutch switch may be bad but you didn’t know that because of the bad neutral switch)
- Try to burn off the carbon ( http://www.gl1000.info/NeutralLight.shtml .) Didn’t work for me.
- Remove the neutral light (bulb)
- Totally bypass everything by removing the bulb and connecting the green with red stripe wire from the solenoid to ground.
- Try cleaning the old switch with solvent (requires removal of the switch.) Didn’t work for me.
- Remove the neutral switch, disassemble, clean contacts, reassemble, and reinstall. I haven’t had success with disassembly, but will be trying again soon.
* but good to know that you've got me covered. 
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