OK, thanks. That really gave me the clue I needed to solve this. I have put the label widget inside a GtkEventBox now, and connect the signals to those. That also helped me solve another problem I was struggling with. To highlight the widget (which display clocks above a Chess board), the foreground and background colors of the text are swapped. But the text did not fill the entire area of the label widget, only the part that was written. By setting the bg color of the EventBox the same as that of the text, I can acheive perfect rectangular highlighting:
