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Are you running the Redline pink milk shake in the transmission?
Nope. Took a look at the engine, gearbox and final drive oil before buying the bike plus the owner had partially filled containers of the fluids that he had put in the bike.
We must also consider the possibility that the new neutral switch is defective. From what I can determine, the switch is supposed to be closed with the plunger out (in neutral) and open with the plunger depressed (in gear). Take the switch out, see if the resistance between the terminal and the shell is near zero, but rises when you push in the plunger. Heat up the switch and then try it again. Before you do that, warm up the bike, then short the neutral switch terminal to ground (engine case). Does the neutral light go on with the ignition? If not, then it's the wiring that's the problem.
It almost sounds like the switch is just <barely> making contact when cold and then when things warm up it isn't. I think I'd try shimming the switch up slightly with a bit thicker washer or shim, allowing the plunger to extend a tiny bit further. Alternatively you could shorten the plunger a bit if the design allows it. Could be the seat where the switch body sits was machined just a touch too deep at the factory....if so the shimming should help. That's what I'd do next anyway.... Terry