[A variant of BATE v.1; in sense 2 perh. of BATE v.2]
1. intr. To bate or flutter as a hawk.
1615. Latham, Falconry (1633), Gloss., Batting, or to bat is when a Hawke fluttereth with her wings either from the pearch or the mans fist, striuing as it were to flie away.
2. trans. (dial. and in U.S.) To bat the eyes: to move the eyelids quickly, to wink.
184778. Halliwell, Bat, to wink. Derbysh.
1879. Miss Jackson, Shropsh. Word-bk., Bat, to wink, or rather to move the eyelids up and down quickly.
1883. American, VI. 237. To bat the eyes, meaning to wink, when we desire to express the rapidity of the action.
1883. J. Harris, in Century Mag., May, 146. You hol your head high; dont you bat your eyes to please none of em.