89 Bronco II 2.9 Eddie bauer

I noticed today that my battery light is on, the gauge shows it is still charging. The needle will show a little discharge but as soon as I give it some gas it will climb up to where it has been prior to this. When the head lights and/or heater fan is on it shows alot of discharge untill I get the rpms up to around 2000 I went to the Haynes manual for help. It gave me some ideal what to do.

First I have used 2 different battery in it one is new and still had the same problem.

The book said:
to check all connections- done everything is good, belt is also new and tension is good.
To disconnect the alternator wiring harness and see if light goes out or stays on- Do I disconnect both plugs? If I disconnect both the light goes out, meaning bad alternator, if I disconnectthe bottom plug light stays on, meaning short some where. Book said if light stays on then start pulling fuses to find the short out circut. Do I do this with the harness disconnected or connected? With it connected I have pulled every fuse on the BII and nothing changed. I have checked the ground wires and every one of them looks good. I have not found any fusible links the book talks about yet.
Electrical is my biggest weak point, any ideals where to go from here or am I doing something wrong.

Thanks

 

Take your Alternator off and take it and have it tested.
With both plugs off it is normal for the light to be off as you can see from the print below.