"fleshy appendage below the neck of certain birds," 1510s (extended jocularly to human beings, 1560s), of uncertain origin and of doubtful relationship to wattle (n.1).
"stakes interlaced with twigs and forming the framework of the wall of a building," Old English watol "hurdle," in plural "twigs, thatching, tiles," related to weðel "bandage," of unknown origin. Surviving in wattle-and-daub "building material for huts, etc." (1808).