Battery light comes on and off

Im stuck. I have a 2000 mustang gt with a stubborn battery light that has a mind of its own. Ive had the battery tested and replaced the alternator. Also tested the battery terminals connections its all good. The only thing that really seems to keep the light off more is if im running A/C. I'm not sure why this would be but it is. Any tips?
 
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We need to what the actual battery voltage is when this problem is happening.

It would also help to know for certain that the voltage drop is within the 0.25 volt specification for the positive and negative side. This will make future trouble shooting more effective.

Howto perform charging system voltage drop test

There could be a lot of little details in a real trouble shooting session of the battery warning light circuit. Not fun if it's not necessary.
 
We need to what the actual battery voltage is when this problem is happening.

It would also help to know for certain that the voltage drop is within the 0.25 volt specification for the positive and negative side. This will make future trouble shooting more effective.

Howto perform charging system voltage drop test

There could be a lot of little details in a real trouble shooting session of the battery warning
We need to what the actual battery voltage is when this problem is happening.

It would also help to know for certain that the voltage drop is within the 0.25 volt specification for the positive and negative side. This will make future trouble shooting more effective.

Howto perform charging system voltage drop test

There could be a lot of little details in a real trouble shooting session of the battery warning light circuit. Not fun if it's not necessary.
The charging voltage is just above 14v and when the car is off its at about 12.6 or so. I will do the voltage drop and get back to you. Thank you
 
More about the car. Underdrive pullies, sct x4 tuned on 91, full bolt on except intake plenum and lower intake manifold. Aftermarket theft protection and aftermarket tachometer. Also ive gotten Camshaft position sensor codes in the past but read on here that if the battery light is on it can throw that code. Abs light is on and haven't looked into that yet. (One problem at a time..)