Evening All,
One brake pad is fixed and the other actuated. Locking it with a grub screw would be my last option.
I think I can see wear on the key in the photo. Changing that would have to be a good start.
How often do you use the brake in anger? Most of the starting and stopping is done with the transmission. If there is only a small amount of play and serious use is occasional then is a small amount of play a problem?it looks like a big key. 1/4 inch square?
Cheers,