Assuming you have an older GM altenator with a built in regulator:..
Also check to see if both wires on the plug get 12V with it running at idle ,it could be the wite or tan wire is not getting the 12V signal from the ignition switch ,that energizes the field coils and makes it start charging..the red wire in the plug is hot all the time..should have power at both wires ..
Its possible for that white or tan wire to be "dead" and yet still get the altenator to kick in and start charging above idle speed ,it somehow "flashes" itself internally after it reaches a certain RPM and activates the field coils..
Many times when I go to check for voltage with a test light on those 2 wires,when I touch it to the white or tan one (#2 terminal on the ALT plug),I'll hear the altenator kick in and start charging ,because the wire was not providing 12V,and my test lamp just DID!...once it kicks in it'll charge normally usually until you shut the engine off,then the cycle repeats..
If the voltage keeps dropping at lower rpms and going up when you rev it,its more likely the belt is slipping..or poor grounds,bad cables with high resistance..