After a few more hours reading and looking at diagrams I've found the issue. A common thread in neutral light posts is that if the light is always OFF, then it is the neutral switch located in the engine. If the light is always ON or Flickering, then the ground wire to the sensor is shorting somewhere. In my case - the sensor leads go into the engine on the left side near where the starter is. The wires follow the frame back to the wiring harness near where the Fuel and Starter relays are under the seat. Simply moving those wires around was enough to get the neutral indicator working as expected. Now to try and see if it's actually grounding somewhere or a dirty / bad connection.