On a deflection into the backcourt, the offense is usually very quick to get to the ball (if they even get it!). It isn't left sitting in the backcourt for 10 seconds. And it would be very rare to have an organized press against the ball that prevented the offense from advancing it across half court before 10 seconds is up, regardless of when you start the count. So reality is it probably doesn't matter.
That said, NCAA or NFHS game, path of least resistance is not the right answer! Start the count when it is supposed to start, not when the coach/fans/players think it should start.
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