Jerry, I remember those well, I think the one we had was Hunter.
The deal with the beads is that the beads is all that is used. It works by centrifical force, as you speed up the beads flow out inside the tire and some how settle at the light spots therefore balancing the tire. Don't even ask, I have no idea how or why, I left college about 5 years shy of receiving my doctorate. Your use of the "original spin balancer" would actually work if you spun up to 40 or 50 mph, left the rings at zero, and wait 30 seconds or so and I'll bet the light stops flashing.
Funny, I was at the tire shop today, and one of the techs loaded a couple new tires in the service truck, went back in the shop and when he came back out he had 2 bags of beads in his hand.
I see I did not mention, it takes about 35 or 40 mph for them to settle in and work.