Don't know about your wire colors but..... the lg stud wire goes to the battery, might be via the starter lug, but it winds up at the pos post on the battery,
The #1 terminal on the pig tail (white) is the exciter wire and goes to the idiot light. The idiot light gets 12v from the dash side and when the alt isn't turning and producing juice, the light gets it's ground from the internal regulator/rectifier.... and lights up. When you start the car the reg/rectifier gets 12v and it removes the ground....light goes out (no ground) and the reg/rectifier tells the alt to start to produce juice.
The #2 terminal on the pig tail (red) is the sense wire and is tied into the POS side of the electrical system and tells the alt how much juice to produce depending on the demands of the elec system, now some people tie it to the lg stud on the back of the alt, but GM originally tied it well away from the alt to take advantage of the resistance of the long wire run and get a truer sense of the demand on the electrical system etc.....
As for your black wire?????? ground maybe