Well, braking shimmy is most likely the thrust arm bushings... mine went away after I changed the bushings... but my 50-60 shimmy is still there... very mild...but still there.
Check your wheels... balancing... out of round.. hubcentric rings (I'm getting a set just to be safe)...alignment.
From what I've read, if you really, really, really, really wanna be sure... you're gonna be rebuilding the front suspension, including steering components... if that still don't work... do the rear... if that don't work... well... you might just have to live with it.
I'm trying hub rings first... if that doesn't solve my mild shimmy... I'm checking some steering components that I might've missed... then check my subframe mounts... then rear shocks... then nothing else seems to be wrong, it might just all go back to my thrust arm ball joints.