Clock, how old are your tires? Old tires can feel that way. As tires age the plies in the tire can start to seperate. The tread can loosen and come off in chunks or all at once.
Before this happens you will notice ride and handleing problems.
The 81 I have had old tires on it. They have very little wear. Some of the mold tits are still on the tread. No cracking. They were made in 1995. As you said , no hands and the death wobble. I swapped tires around from the 75 and the parts bike and the wobble almost disappeared.
I now have a new set of tires and it rides and handles great.
The tire manufacturers don't reccomend running tires over 6 years old. Reasons as described above. If you remember a few years ago there was a big thing about SUV's flipping over and people dieing. They found that the tires on these SUV's were very old. Even if they were just put on as new. The tv reporters did a search of tires at tire stores and found tires up to 14 years old still on the rack and being sold as new.
The old tires were failing and causing the rollovers.
To tell the manufacture date of a tire you look at the DOT number on the tire. The DOT number has an oval with 3 or 4 digits in it. These digits tell the week and year of manufacture. The first two represent the week the third and fourth tell the year. If the oval has 3 digits the tire was made before 2000, 200 and adfter have 4 digits.
The tires on the 81 were dated 275 on one, 405 on the other. This means the tires were made the 27th and 40th week of 1995. The tires I put on read 1310 and 1610, as in 13th and 16th week of 2010.
AS xjwmx said check the swing arm for play. To check the play put the bike up on the center stand, pull the shocks, and rear wheel, now wiggle the swing arm back and forth sideways. If it moves, the bushings might be worn. check the torque on the swing arm pivot bolt. If less than about 50 ft/lbs it won't clamp the pivot tube between the frame sides and allow excessive play.
If with proper torque on the bolt and you still feel movement over .004, thats the spec in the book. If you can feel much play replace the bushings.
On the 81 the threaded part of the pivot bolt was broken off. A PO had drilled and tapped the end of the bolt and put a 5/16 bolt in there to hold it. It didn't work very well.
I pulled it all apart to replace the bushings. I found that the pivot tube fit very snug in the bushings. Even well greased I couldn't slide it in by hand, I had to tap it in with a mallet.
I used the pivot bolt from my parts bike and put the swing arm back in the frame. I then torqued the pivot bolt to about 45 ft/lbs. If I lifted the swing arm up to level , it would drop back down when I let go. I increased the torque to 50 ft/lbs. Lifting the releasing the swing arm it would drop slower. At about 55 it would hold position. I torqued to 65 and it would stay up and took a few lbs of push with my hand to get it to move. So I put it all back together with the stock bushings. Feels great in the corners.
So if you suspect the bushings are worn check the pivot bolt torgue. It might just be loose.
Leo