Sorry, couldn't resist that one.... ;)
OK, so it wasn't the Alternator light that was on (I'm jealous - you have an e-brake-on light, too??)
Let's see if I have this straight, Ron (and I bet Ron O gets his students to help on the tough ones):
1. The alternator is putting out 13 volts - that's good. It's supposed to be in the 12.5 - 14 range so 13 volts is nice. If it keeps your car running after you pull the battery lead then (technically) it's providing enough power to run your ignition, but you don't know if it's capable of charging your battery. However! Since you don't have a dead battery, chances are it's charging OK, so don't worry about it.
2. In an earlier post, you said that you tested the voltage at the "reg. lead" which Brian and I assume is marked "D+" (the small wire on the alternator with a 1/4" fast-on connector). If you're getting 12V there, then chances are the dash lamp is OK, since you're reading voltage THROUGH it. Another way to test the dash lamp is to remove the D+ lead from the alternator and ground it - the dash lamp should light when the key is "on". If not, change the lamp, or check the wiring, or check the brushes - see earlier posts).
3. When the car is running with the battery connected the alternator light is out. That's good. It's supposed to be out if nothing is wrong, and it doesn't sound like anything is wrong. Your battery is charged enough to start the car (the most load you can give it), and if the dash lamp were burned out the alternator wouldn't be charging ('cause it gets its charge signal through the dash lamp, right?).
4. If you turn on the ignition and don't start the engine, the alternator dash lamp should illuminate, 'cause the alternator isn't generating a back voltage to put it out. Your Oil light should come on, too, but that's another story. This is kind-of a cheapo lamp test (and all you ex-military pilot guys know what lamp tests are!!). If it doesn't light with key on and engine stopped, then something's wrong - lamp burnt out, mis-wired, wrong or partially failed bulb (might light too weak to easily see, but still passing a signal to the alternator - BTW, this is a way to adjust the output of the alternator.....different lamps have different resistences and give different signals to the alternator circuit, but that's another story, too!
So, does this help or should I just keep quiet?