In order to reproduce the issue, we needed to turn off System Preferences > Mission Control > Displays have separate Spaces. In that case, if you move the mouse to the very top of the screen and click, the counter on the above composition does not increment. If you move the mouse down just one pixel, then clicking does work.
Ahhh, yes I have “Displays have separate Spaces” disabled since I need to ensure the menu bar and dock never pop up, for an exhibition.
This is the other characteristic of exhibitions, the public will find any bug or chink in the armor. :-)