Both my mirrors were shakey! Based on this thread, I used a little right-angle ratcheting Phillips screwdriver and tightened the three Phillips head machine screws, and all seems to be good! The mirror head itself is no longer loose, and a quick road test showed no glass shake. Fingers crossed!!
Thanks to you previous posters for the tips! (The worst part is getting up the nerve to pop the plastic cover off the bottom of the mirror. :eek.: )