I know my battery was dying so I replaced it. A few days later the battery light came on, and based on numerous threads here and on other forums, I decided to replace the alternator. The voltage at the battery was 12.5V off, and almost 12V with engine running. Seemed reasonable, alternator not producing power.
Well the new one didn't help. So I started checking the wire harnesses and eventually found a broken wire beneath the brake master cylinder. It had corrosion on it, as if the master cylinder leaked on it. I confirmed via a volt meter that the yellow/white broken wire was from the alternator.
Anyway, fixing the wire corrected the problem.
Battery light now off, voltage at battery while engine running is again 14+V.
Sadly, the alternator I returned as the exchange core was actually good.

 

That's why you should have the alternator bench tested before buying a new one. Far too many people waste money by skipping a step. Glad to hear you found the correction though.