That smaller wire is connected to the field coils. It goes to the "F" terminal on the voltage regulator. There also needs to be a third wire (ground), connecting the generator housing to the regulator base. By intermittently connecting the field coils to ground and opening the circuit with two sets of vibrating points, the current and voltage output of the generator is controlled within pre-set limits. This prevents generator overcurrent damage or overcharging the battery.
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!