by 1912, American English (said in original citation to be a Kansas City term), from jay, perhaps with notion of boldness and impudence. Related: Jaywalk; jaywalker.
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jay n.
the common European jay (Garrulus glandarinus), early 14c. (late 12c. as a surname), from Old North French gai, Old French jai "magpie, jay" (12c., Modern French geai), from Late Latin gaius "a jay," probably echoic of the bird's harsh warning cry and supposedly influenced by Latin Gaius, a common Roman proper name.
For other bird names from proper names, compare martin and parrot. Applied to the North American blue jay (Cyanocitta cristata) from 1709; it is unrelated but has similar vivid markings, is noisy and restless, and also has a harsh call. Applied to humans in sense of "impertinent chatterer, loud, flashy dresser" from 1520s. Jolly as a jay was a Middle English expression for "very happy, joyful."