take another look at those wires. The neutral switch is a simple circuit. 1 wire - typically light green/red. It will go from the actual switch to the head light bucket where it plugs into the wire that goes straight to the bulb. The bulb will have 12v black wire coming from it. When in neutral, it grounds and completes the circuit, lighting the light.
Sound like you may have a starter motor safety unit ? If that is the case, I think that wire is a darker green/red. If you have those switched, it looks like you would light the lamp as well.