What is the meaning of the word "bat"?

Definitions:

in baseball, a turn trying to get a hit noun
- I was at bat when it happened.
the club used in playing cricket noun
- a cricket bat has a narrow handle and a broad flat end for hitting
to have a turn at bat verb
- Jones bats first, followed by Martinez.
to strike with, or as if with a baseball bat verb
- I bat the ball.
to use a bat verb
- Who's batting?
to wink briefly verb
- They batted their eyelashes at me.