Read through everything first. Its complicated but not.
So the sequence of the "ball" taking awhile would likely be based on the ball getting caught up in the return trough. I am not sure which switch is the one in question, but there's an internal timer within the game that knows to differentiate between a strike and ball.
You can ONLY get a strike if you swing, OR have more than 3 balls and not swing(or 3-0 baseball term for ref). With that being said if you foul hit a pitch, the game will recognize the fact you swung and dish out a strike. However if the internal timer runs out (Roughly 2 seconds) it will dish a ball (typically when a foul actually happens). What's likely happening is maybe a couple things? It could be the switch, you're getting phantom strikes on and is stuck closed and creating a switch ground, OR the switch could be flakey, and not register the ball crossing over it. We assuming the switch 52 is the return trough switch.
When the ball reaches the end of the trough, the pitch buttons are supposed to re-enable by flashing. While the game is between figuring out strikes and balls, the pitch buttons stop flashing, letting you know the game is "busy". If you continue to try to pitch, the game will not let you do so if the buttons are not ready or flashing. Thus you will sit here hitting the button to pitch, and waiting for the game to be ready to pitch the next ball despite the ball already being where it needs to be. The game will then timeout another timer that allows play to continue. And that's what you are waiting for.