The inside rearview mirror flopped a bit, and pulling the assembly off, I noted the ball was not loose in the mirror body - it was loose on the support stem. It had a shaft cast with the ball, which fit into a hole in the support stem - secured by unknown means.

To repair, I slid the soft trim coating down the stem away from the ball, then drilled a small hole radially through the pot-metal stem and into the ball shaft. I screwed a miniature sheet metal screw into this hole, fastening the loose ball shaft to the stem. I then grabbed the screwhead with a visegrip, twisting it further in until the exposed part twisted off flush with the stem. I then let the coating slide back over the repair, leaving no trace. The mirror now works like new. It took about 10 minutes.

Steve