Vacuum Leak?

Could be wrong, but it sounds to me like you have a vacuum leak around the throttle shaft. By partially covering the air inlet with your hand, you are restricting the airflow through the carb enough to make the air leaking around the throttle shaft even things out and you get the correct idle mixture and a nice steady idle. Removing your hand lets it go lean and want to die. See if you can wiggle the throttle shaft up and down and front to rear. If you can there are probably some bushings and a new throttle shaft in your future. There should be next to no detectable movement in the throttle shaft when you wiggle it back and forth. Hope this helps.