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Indeed, I didn't think about the fact that the timer can't be stopped during a battle now. So, yes, we'll have to start the countdown only after a turn is taken, otherwise it won't work.
We need to ask baratorch to come up with something like that... what if both players press "pause" at the same time, the time would stop for both. Or maybe it could be that a player can stop the opponent's time... then, if someone needs to step away, they warn the other player, and after completing their turn, they pass it on and press pause.