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1580s, from French moustache (15c.), from Italian mostaccio, from Medieval Greek moustakion, diminutive of Doric mystax (genitive mystakos) "upper lip, mustache," related to mastax "jaws, mouth," literally "that with which one chews," from PIE root *mendh- "to chew" (see mandible).
Borrowed earlier (1550s) as mostacchi, from the Italian word or its Spanish derivative mostacho. The plural form of this, mustachios, lingers in English. Dutch slang has a useful noun, de befborstel, to refer to the mustache specifically as a tool for stimulating the clitoris; probably from beffen "to stimulate the clitoris with the tongue."