Thanks for the replies.
M.B.Doc, I've had the shifter bushings replaced about 20K miles ago, and don't really have any appreciable play. I am still convinced there is some sort of electrical event happening here. When I'm in Park and hit the brake, the click coincides with the shifter rod being able to be moved out of Park. It's the same sound/feeling when I hit the brake while in any gear -- same click. Even though a cable is used, I assume there must be a solenoid somewhere? I'd assume that the trigger for the solenoid would be getting current from the stop light switch . . .
In any event, my main concern is: Is this normal? If not, is it hurting anything if left alone?