jay: [13] Like the robin, the jay may have been christened originally with a human name; Latin Gaius. At all events, the term for it in postclassical Latin was gaius, which passed into English via Old French jay. The term jaywalker for ‘one who crosses the road illegally’ originated in the USA around the time of World War I; it was based on an American use of jay for a ‘fool’ or ‘simpleton’. [jay etymology, jay origin, 英语词源]
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.