I think I fixed it. I put the coil that was in it when I bought it 37 years ago and also a condenser that I had previously removed just because. Before I did all of that, I took the dist. cap off and noticed that I would get spark at the points right away but it would go away in just a few revolutions of the cam so I figure one of the replaced components was bad. While I was doing all of that I thought I might as well clean up the points so I took them off. The part is a Blue Streak and it had a felt wiper built into it to clean or lubricate the cam. What it didn't have was free movement and I found that the spring loaded arm would not close all the way (the points remained open) and that it moved with difficulty. So I found a set of points that I had removed previously (just because), cleaned up the contacts and put them in. It has been idling in the driveway for about 45 minutes with no issues.
I do notice that the carb is wet after driving but dry after idling for so long. I got my rebuild kit yesterday and will do up the replacement carb that hopefully will not leak. Thank for all the advice and comments!