YS4500 shorting starter works directly wired switch wont.

If there is not a separate relay: If it only starts when connecting the 2 large wires on the starter, but not when connecting a hot wire to the small wire from the solenoid that goes to the ignition switch, there are possibilities. Either the small wire from solenoid to ignition switch is broken, or the solenoid is bad. Try connecting the small solenoid wire to a hot wire. If that works, but it doesn’t work when you connect a hot wire to the solenoid wire at the ignition switch, then replace wire from switch to starter solenoid. If a hot wire to the solenoid gets no response, the solenoid is bad and you probably should replace the starter. If both of the above things start the motor, the ignition switch is bad.

If there is a separate relay: Perform same test (above) except the wire from the ignition switch will go to the relay instead of the solenoid. Try connecting hot wire to small wire on the relay. The relay should make a click sound. If not, the relay is likely no good. If you connect the 2 large wires on the relay, the starter should turn and start engine. If starter spins but does not turn engine, the solenoid is bad.

Solenoid: Pushes out the starter gear so it engages the flywheel

Relay: A remote switch that handles more current so the current of the starter does not flow through the ignition switch. The relay is often mounted to the starter or built into the solenoid.