...Can anyone refresh my memory and tell me in what scene Celes wore a party hat?

I think its a reference to a summoner class? summoners in FF usually have robes and a horn

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Put drill on head

Not even Celes knows where the drill hat came from.

Hm... Did...did Edgar...drill Celes?

there was a glitch back in the japanese version of the game where you could equip any item as a helm, and apparently the drill was the best hat.

GARamonde indeed