I've been using an attachment for guitar pots that screws atop the pot
and allows the cleaner to squrt down the shaft. Saves a lot of time in
some cases and can be used on anything with a similar pot.

Where do you find these?
I assume they're "custom" and won't work as well on a smaller shaft.

Most guitar supply places have them. I think we get them from WD
music although I was not the one who ordered them. And I'm fairly
sure they make several sizes.

There's a Guitar Center (or whatever it's called) down the road. I'll check
the next time I'm in the neighborhoods.