Oh, and I forgot to mention that pause had to be synchronized across the network, so the pause button would pause for all players.
And in the "this is why we can't have nice things", that also introduced problems, because we didn't want a player who was losing to keep pausing the game until the winning player quit out of frustration, so I think we kept a per-player pause counter, which would only be restored if other players also paused? (I don't quite remember all the details, just that we had to prevent yet another abuse vector).
I remember something like this back when playing StarCraft (maybe Brood War, it's been a minute) online.