It seems that for Response type windows, MinBox is greyed out and even if it appears checked, there is never a minimize control on the window.
Is there some API way perhaps to override this? The tricky part would be that if the response window was minimized, really all windows it popped up up from (which could be more than 1, in a sequence of Main, then Response, then Response ...) should be minimized. And when the app was then restored from the taskbar, the windows would all have to come back the way they were.
Thanks.