The four relay circuit should work in the following way.
Bike in GearIf any gear is selected on the transmission, the TGPI switch will have one or more wires open circuit. In this state, one or more relays 1, 2 or 3 will not be engaged. Therefore the output on relay #3 to the Black/Green wire will be off and the start circuit will not work. At the same time, Relay #4 receive no power on its coil and it is disengaged as well. The Neutral light is open circuit in this state; no current can flow through Relay #4 contact to ground. The Neutral light should be off.
Bike in NeutralWhen the bike is in neutral, all three wires from the TGPI switch are grounded; relays 1, 2 and 3 are all engaged and +12V is delivered to Black/Green wire and Relay 4's coil. The bike can start without the clutch pulled in because +12V is now applied to the start circuit. Relay 4 is engaged because power is applied to its coil. Current can now flow through Relay 4's contacts to ground and the Neutral light will turn on.
This circuit ASSUMES the neutral light in the speedo is an LED and had one side connected internally to +12V. If this is not the case with your speedometer, you will have to tell us what the manufacturer expects for the installation.
Turns out I may not have everything right. I've tested the circuit with a 9V battery and it seems to work. When I put 9V to 30/86 on relay one and ground 85 on all three I get 9V on 87 for relay 3. Disconnect ground from 85 on either relay and I get no output. This is correct right?
That seems to be correct based on your description.
* green/black to relay 1 30 and all relays 86
* yellow/blue to relay 1 85
* yellow/black to relay 2 85
* yellow/white to relay 3 85
* black/green to relay 3 87
Your wiring list is correct for a 3-relay circuit. The fourth relay and the diode are required if you want a neutral light.
If you'e not getting +12V at the start switch with the clutch pulled, then you may have a defective fuse #1. Maybe your kill switch is engaged?