Chronically Tardy

You and your cousin grew up in the same family, but time management has never been his strong suit. Always the last one to arrive, he has a knack for keeping everyone waiting. This has been a sore point between you, as family gatherings are important and his constant tardiness has become a running joke. Today, during yet another heated argument about his poor timing, the lights flickered and you both found yourselves in a room, a sign on the door reading: 'Resolution or Perpetuity!'.