It seems to be when you, flip the run switch. That's when there's a voltage drop, hence the neutral light dimming. ( it's under load supplying power to the ignition/coils) 1st... don't flip the kill switch, leave it on...turning the kill switch on and off, in most of the causes, of non running bikes, turn the engine off/on by the key. There's an intermittent fault, in the head light, or the ignition switch, under load. It seems that something is getting, hot then braking down. That's why it works then stops, then works again.
Go down to harbour fright, and get yourself, a volt meter. and some wd40 or same as. Then check the voltage, you might have a brake in the insulation, that makes, then gets hot, then brakes, then makes. In the head light.
Unplug, some of the large plugs,(one at a time) and spray inside, (both sides) then push back together (a tight fit) you might find that there could be something not making, causing this problem, and come away in your hands?

At least you found it!! Let us know how you get on, and any, photo's of the burnt whire/s
