Alternator not charging

First, with the engine off, measure the voltage on the large output stud on the alternator. You should find full battery voltage there. Next, do a continuity test from each of the two smaller wires, to ground. One should read 0 ohms, plus whatever is in your meter leads. The other one should read roughly four ohms more. If you get an open circuit reading for only the second small wire, irritate the belt and pulley a little. It is common to have a poor connection when the field winding is not spinning. That can falsely show the brushes are worn. That second wire is the brown/gray wire.

With the engine running, measure the voltage on all three wires, and tell me what you found.