"On the Ball" originates from a brand of pocket watch. The Ball Watch Co. became synonymous with precision and punctuality after its railway watch carried by conductors largely standardized railway timekeeping.
The Truth About The Ball Railway Watch
https://thetruthaboutwatches.com/2020/04/the-truth-about-the-ball-railway-watch/
Here's "Balls out" or "Balls to the wall." It came from steam engines....
https://www.youtube.com/watch?v=zfDYgMfuEvY
https://www.watchuseek.com/threads/get-on-the-ball-does-this-relate-to-ball-watches.298802/