Thanks for all of the posts guys. That is exactly what I wanted to see, past experience.
I've had the typical old battery problems before with other cars, but I never saw one that would start the car just fine, over and over, yet when your driving it (read that when it is charging) with the lights on, the battery goes dead.
I still question the charging system. The car is idling just about right 750rpm (In park), I don't think the charging system should be producing it's maximum output at this speed. From the other posts I've read the voltages should start to go up at about 2000rpm. Note I had no change at all when increasing rpms.
Terminal connections are clean and tight. I am going to trace and check the wiring. If I don't find a definitive answer I'll probably replace the battery, alternator, and voltage regulator.
I bought this car for my wife to drive and for me to fix. (gets me out of the office) It's really not a daily driver so I expect I will replace everything by the time I am done. I did a lot to it over the winter and we thought we would drive it on the few summer days we have, so I don't want it to leave her stranded.
Thanks again for all of the information.