light green/red goes from the neutral switch to the neutral lamp and the diode in the fuse block on the handlebars where it connects to the green/red wire via the diode. The green/red wire starts at the switched terminal of the solenoid (not the 12v+ terminal) and goes to the clutch switch and to the diode which allows only one way current flow. This ends up with two switches in parallel that can independently allow grounding of the solenoid.
The yell/red wire from the start switch connects 12v from the black wire on the start switch that comes from the ignition switch.
So, for the starter to crank you need the ignition switch to connect the battery to the black wire, the start switch to connect the black to the y/r wire, AND either the neutral switch grounding the light green/red wire OR the clutch switch grounding the green/red wire, or Both can be grounded.
Al of these various switches need to be clean with secure connections. Use a volt ohm meter and follow the circuits, look for voltage drops and corroded connections.