Coach, the 10 second backcourt count does NOT reset when the defense causes the ball to go out of bounds.

Does a timeout reset the 10 second count?

The ten second count is reset if the team calls a timeout or if the ball becomes dead.

Does the 8 second count reset after a timeout?

The count begins when there is player control in the court; if the ball is deflected out of bounds (or if play is stopped because of an injury to a player of the team in control) the count is not reset: the official will show the number of seconds remaining before handing the ball for the throw-in.