While you can push pause and it will stop the clock from counting down, it won't actually stop the next segment from coming. In the _start_pomodoro function:
will cause the next break segment to start no matter what, no matter how long you have it paused for.
I know this would take a big change in the way that you operate the program to fix, but I may suggest that if you ever find a way to implement the buttons, pausing may not ever even be necessary in this program.
While you can push pause and it will stop the clock from counting down, it won't actually stop the next segment from coming. In the _start_pomodoro function:
Mainloop.timeout_add_seconds(Pomodoro.time_limit / 1000, go_pomodoro);
will cause the next break segment to start no matter what, no matter how long you have it paused for.
I know this would take a big change in the way that you operate the program to fix, but I may suggest that if you ever find a way to implement the buttons, pausing may not ever even be necessary in this program.