Usually up to 15 minutes prior to park closing. BUT... there are exceptions during irregular hours, special events (like party nights, etc) and during EMH so you do need to check. If you are wanting to make an ADR and you know the park closes at 6 that night, try putting in for a 5.30 or 5.45 ressie and see what comes up. If you have no joy, call as soon as the phone lines open. Hope it works well for you.
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