SFO flight at 12.20 p.m. is one of the latest flights so the rush should have passed. The TV screens ask you to hold in the shopping/food area and they flash up when preclearance is open for a particular flight, usually two hours before hand. As far as I know they won't process you until the flight is officially open. If you are really worried then I'd say if you are at security around 10 a.m. that should be fine.
There's a short video at the link below that will help if you've not done this before.
US Preclearance