The convention for GNOME games with timers is to have a play/pause button to
allow the user to stop the clock. This will draw an overlay over the board so
that the user can't see the board while the clock is stopped.

Some games also stop the clock when the window becomes unfocused, but I think
I'd like to shy away from this since it can be pretty jarring if you're opening
the app menu, for example, or if you actually do want to look at the game while
the window is unfocused (which is more likely to make sense for complicated
games, like Chess and Sudoku, more than others).