My shower faucet handles are Elger shiny chrome 1 piece handles.
Shaped like a fluted ball with a cylinder beneath it.
They have no screws holding them on.
They do have a small rectangular "cross pin" looking thing.
It can't be driven out, and it may be a spring that snaps in an indentation?
There's not enough clearance to see how it functions.
They are loose enough to rock, have some play, probably by design.

I'd like to get the handles off and replace the faucet, but have not figured this out.