Odd charging issue

[cwh19]

94 gt with the battery in the trunk. When the cars off, battery reads 12.6v and the alt reads 12.4v. When the car is idling at approx 1k rpm, the battery reads 12.06v and the alt reads 11.94v. The battery light is on. Pullies are factory size.

Thoughts?

[mustang50lx]

Sounds like a bad alternator and maybe a bad connection too causing the voltage drop.