clutch safety switch

If the relay only has one "push on" (spade/ flag) terminal, then your start problem is elsewhere, unless the relay is bad. MAKE SURE the relay is grounded.

The green going through the firewall "to the inside" is going to the switch, so that's the "dead end" side of the circuit

Circuit path is "from ground"..........through switch.......green wire......out through firewall........to one terminal of the relay......through relay coil.......out on the other terminal to the yellow start wire........through the firewall via bulkhead connector...........to S terminal on ignition switch