The Luminary class is not available at the start of the game and must be unlocked by an in-game quest.
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Luminary cannot be unlocked until the main story is completed. To unlock the luminary class, you have to go to the dance club in Gleeba. Go over to the left side, near the girls' makeup room and talk a girl named Applaudia. She tells you to kill a moai minstrel with the hot lick ability. After doing so, go back and talk to her to unlock the luminary class.
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The Luminary class has access to the following skills:
Fan Skill - use of fan-class weapons.
Whip Skill - use of whip-class weapons.
Boomerang Skill - use of boomerang-class weapons.
Shield Skill - use of shields in the off hand.
Je Ne Sais Quoi - the class-exclusive skill set of the Luminary.
Their Coup-de-Grace is "Disco Tech," which causes all enemies to boogie and raises tension by one level.