Upgrades clear at the time of request only if there is upgrade inventory available. Otherwise, you go on the waitlist. On the premium domestic routes like JFK-LAX and JFK-SFO, upgrade inventory is, for all practical purposes, never released before the gate. The agent should be able to tell you at the time of booking whether or not there is upgrade inventory available for you to clear immediately. A subscription to ExpertFlyer will also give you this information.

So plan to not get the upgrade until 30-45 minutes before departure.

On the day you check in: A properly coded SWU will put you up near the top of the upgrade list. You are above all other passengers waiting for complimentary upgrades, and can only be topped by other medallions who used a SWU or other passengers who paid for BusinessElite but were rebooked in coach (usually due to IROPS). If you check in and see yourself far down on the list, it's worth a call to ensure your SWU was coded properly. The agent should be able to confirm your upgrade priority as "UP2B", which is the priority code for a Platinum Medallion waitlisted for a SWU upgrade. If they say your upgrade priority code is UP3, that's your complimentary upgrade priority and it indicates your SWU was not properly applied. Ask them to fix it.