battery light comes on mazda tribute

2001 Mazda tribute v6 with a NEW alternator. Will start from beginning to be clear. Original alternator went out 3 years ago. Was replaced with after market, this worked for 3 years, was replace with another was told this one did not charge correctly ,was replaced with a NEW Bosh. Still the problem does not charge correctly. Charges when first started when it warms up with heat,radio,lights etc on only charges 12.8-12.9, rev it up charges high 13′ drops back down when car goes to normal idle. Was not the fans ,connections good ,all wires good and checked out fine when car hooked to there diagnostic machine. Sometimes when I go to start it it swipes all gauge needles to the right and just clicks. put charger on a few minutes it starts.

Edit for follow-up:

Everything has been checked. NEW Bosch alternator installed. Charges 12.9 with everything running . There rep is telling garage it is the cooling fans drawing to much when they kick into high. Never had this problem before owned the car for 7 years with orig. alternator. changed that all needles would peg left and car would not start. Battery light never came on. The replacement was good for two years. Then same thing started with needles pegging. They put on after market rebuilt again thats when battery light started. Have now drove it 2 weeks with New bosch and have not had a light come on. They are checking the cooling fans for draw. I do not believe its the fans. Think it was the second replacement that was no good. How could it be the fans now and not have happened in 9 years

Edit for follow-up:

Now with NEW Bosch alternator, was not the fans, No battery light comes on, Pegged the needles once and didn’t start put the charger on for a few minutes starts right up. But still shows it is only charging about 12.8 when warm and things running. Rev it up and it charges then drops off again when back to idle. Tested other car and it charges around 14 at warm, things running and at idle was told thats what it should be. Checked all connections, wires and fuses.Battery does not lose charge over night. I Do not believe it is the alternator.