The smaller gauge wire is a grounding wire for an idiot light, if you choose to use one. It's also used as an excitation lead to turn the solid state voltage regulator on if you choose to use it that way. Otherwise, it might be necessary to rev the engine up once after starting before the alternator will begin to charge. If you don't choose to use an indicator light and connect the small wire to the ignition system, it's possible there will be enough feedback to the ignition to keep the engine running when the switch is turned off. To prevent that from happening, use a 100 ohm resistor or a diode in the wire to block the feedback current.
Jerry

"It is better to be silent and be thought a fool than to speak and eliminate all doubt!" - Abraham Lincoln
Cringe and wail in fear, Eloi- - - - -we Morlocks are on the hunt!
There is nothing noble in being superior to your fellow man; true nobility is being superior to your former self. - Ernest Hemingway
Love your enemies and drive 'em nuts!