The alternator will keep the car running and driving, with headlights, wipers and heater on. the battery drained in less than ten minutes of drive time on a 100% charge.
This proves nothing. What is the ammeter doing while all this is going on? The alternator may only be capable of putting part of its rated output, I.E. it may have a problem
DO NOT EVER disconnect battery cables from a running car. I wish I could bury this old wives tale. You will NEVER read about, or be taught this in any class, text book, shop manual, or tune up course.
12--13V is LOW
DO you have a shop manual?
Download one here:
Scroll down the pages, somewhere in that thread is a link to a 66 manual.