Thanks for your suggestions, Mr. Muskrat. I considered solutions where I forced the mouse to move with MouseMoveAbsPix, but I would rather simulate the click events without moving the mouse if I can. The user would be distracted and annoyed if I take mouse control away.

My status window is just a simple one with a Tk::ProgressBar and a text string in it, so PushButton won't work. SendKeys may be my best option. Keystroke events are a bit of a pain because sometimes another window takes the focus and gets them, but they may be the best I can do.