It has a 'ball joint' where it clips into the piston of the master cylinder, so it should "move around" but it shouldn't move in and out much.

If there's not a groove worn in the actuating arm you can get the clip in the "HELP" section of most autoparts stores. Dorman/Motormite P/N 14041
It's an assortment, you only need 1 of the 5, but it's readily available.
You put it in the hole first and then pop it on the lever, otherwise you'll destroy it trying to get the "eye" over the fingers.