If you've got an '85 or later 60, maybe replace the slave cylinder with a Toyota slave. Not aftermarket.
These models of cruisers' slaves apply constant pressure to the throw out bearing with an internal spring. If the spring is weak, the bearing friction surface can slip on the clutch spring tangs instead of grab it to spin the bearing. ... making a squeaking noise.
I had an aftermarket slave that did this. When I replaced it with a Toyota slave, the squeaker went away. Squeaking was worse in the morning until the bearing warmed up and could spin more freely.
Replacing the T.O. bearing is a big job. Tranny has to be dropped.