On the back of the alternator there should be one brush in an insulated holder. Green field wire attaches to the terminal on it.
If there is a second insulated brush with a terminal on it, that needs to be connected to ground.
On pre-1970 alternators, that second brush is in a non insulated holder and attached to the alternator casing. Those are don't require a grounding wire since the esecond brush is grounded to the case.
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picture from here