Brake pedal play

Let me start with I have no issue with the operation of the brakes. What I am getting annoyed by is the looseness of the physical pedal once I take my foot off.

Say I am at a complete stop, foot on brake as needed. Lift foot off normally. Pedal kinda wobbles and makes some noise...not a squeek, more like just the pedal/mount rattle of some kind.

My initial look just got home and tossed the e-brake on while on the flat driveway and actuate the pedal by hand. It just seems a little loose how it's mounted. Anyone have this behavior and any idea on fix?

I need to look at it again and see if I can perhaps shim it but thought I'd ask around first. It's the brake pedal so I don't wanna mess with it much.