That wire is to bring the full 12V to the coil, rather than the dropped voltage after the ballast resistor, during starting (cranking) only.
it brings 12 volts up to the ign switch where it is connected to the green wire returning to the coil. once you stop cranking the coil is only fed from the dropped voltage from the resistor. So you don't need it if you 1) don't want the full 12 V to the coil while starting (might be harder to start) or 2) find a way to do that with additional contacts on your button switch.
