Pause would not affect anyone else in the queue. If you are paused, you are not available for a party and your spot is taken by those who are active. You could be removed from the display of the partially filled party if that is needed. When you un-pause, you get added to a party if there is room or get put with the next party, according to your wait time.

Withdraw is a big penalty to go take a leak when waiting 30 minutes or more for a party.

You would not be able to pause if the party had filled and you were being asked to confirm. The only options at that time would be confirm or withdraw. Pause would only be available while in "Readying Duty" phase.

I'm sure there are other fine details that could be added by the clever designers at SE.