UK, 1820—to show willingness to enter into a contest or take up a challenge, especially in business or politics—originally (1804) used in boxing with reference to the custom of throwing a hat into the ring to signal willingness to enter a contest
The adjective ‘living’ is an intensifier, and ‘daylights’ is an 18th-century slang term for ‘eyes’ chiefly used in contexts of physical violence or threats.
first recorded in The Biglow Papers (1848), by American author James Russell Lowell—based on the notion of leaving one’s hat behind in a rush of impetuosity
USA, 1891—a passenger in the rear seat of a car who gives the driver unwanted advice; hence, figuratively, a person who is eager to advise without responsibility