[Tru_in_Blu]

J. The pitcher has 10 seconds to release the next pitch after receiving the ball or after the umpire indicates "play ball".
Technically, the rule doesn't stipulate anything like "whichever comes first/last".

Obviously, the defense would argue that it's 10 seconds after the pitcher gets the ball, regardless of which circumlocation the ball may have taken. The catcher didn't throw it to someone other than the pitcher, which would result in an automatic ball call.

If this was the first time in the game that it happened, I'd be inclined to warn the offending team.

If it was a situation where the tone of the game had been developing for a few innings, and the pitcher was being a Richard Cranium, I might just decide to call a ball. In all likelihood, walks to the parking lot might follow.

As a UIC, which I'm not, I'd probably rule that the defense intentionally allowed their 10 seconds to be squandered, and that after some seconds had passed and the umpire called "Play ball" [to start the 10-second count-down], they should have hustled to retrieve the ball and make the delivery.

Might also depend on the level of the participants. The 12U crowd often has a bit of trouble with the simple task of a catcher retrieving a ball and making a catchable return throw to the pitcher. And even at that, there's no guarantee the pitcher can actually catch the ball.

So in summary: it depends. Right up there on the fence.