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Fairies in Neverland don't wear pocket squares.
Pocket squares are mostly a question of fashion, image, etiquette, ranking, "codes", sometimes of activities, professions, events, myths, novels and/or movies, etc.,
(Sean Connery, for instance)
and here's a "guide":
https://parisiangentleman.co.uk/academy/dirnellis-ten-commandments-of-the-pocket-square/