[Redmist]

Do you have a multimeter with you that can measure resistance?

What we need to know is: What is the ohms reading of the blue/black wire when measured to a known ground point, when the bike is both in neutral and when not. I imagine the resistance is high when not in neutral, and becomes lower when not in neutral.

The existing neutral bulb is being switched to ground in some way within the neutral switch in the gearbox.

So the old bulb has 12V on one side of it all the time, then when the bike is in neutral the resistance must be lowered so the current can flow thru the bulb, enough to illuminate the bulb.

Now you have an LED, the resistance will be permanently low enough to have the LED lit up.
Is the LED changing brightness when you switch out of neutral?