I was just in my 1967 580 CK. You'll have to pull the shuttle cover to have a look-see.
Mine is the mechanical shuttle. It sounds like it could be worn shaft detents.
In the picture, it's circled in white. You can see a couple of the detents, (grooves).
There's not much on my tractor that hasn't been broken and welded, and under the cover was no exception.
When you pull the shaft out, cover the hole over the shaft in the housing, again the welded part in the circle, because there's a ball under that hole with a spring behind the ball. If you pull the shaft out fast the ball may go flying.
Check the shaft for wear.
I couldn't get my shuttle cover back on and get the forks down over the gearing.
I had to remove the gas tank and loosen the steering tower and pull it forward so I could drop the cover straight down into place. It was actually a good thing because my gas tank was so filled with rust and scale I don't know how it was running.
If anyone knows a way to get the cover back on easily please let me know.
Hope this helps you.