That purple wire runs off the side of the starter switch (the on on the starter that the foot pedal operates) up to the Start terminal on the ignition switch. When the pedal is depressed, it closes both the starter contacts and a second set of contacts for the purple wire. This bypasses the normal power for the coil (green wire) and bypasses the resistor also. The resistor is wired in to the circuit going to the col to cut the voltage down, usually about 6.5 volts or so, to keep the coil from overheating.
You'll want to check all of the connections, both at the dash switch, but also at the resistor itself. Checking the coil wires wouldn't hurt either.
