[BktBallRef]

I understand your points, based on the information available in the case book and rule book.
But, I don't see where the clock must start before a timeout is granted. Does the book say that somewhere?

It doesn't say that the clock has to start. But it does say that a team has to have possession before a request can be granted.

We had a dead ball request for a time out before the team had control and an immediate TO called when that team got control. With immediate being as fast as it is, and with no rule that a team cannot request a timeout on the basis of if..., why can't we call it with no time used?

You have to start the clock as B can't gain possession without the clock starting. The clock has to start. 5-9-3 says If a free throw is not successful and the ball is to remain live, the clock shall be started when the ball touches or is touched by a player on the court. Nowhere in the book does it say that the clock will not start if a team has requested a TO prior to gaining possession. Since the clock has to start, you have to allow the timer one second to stop the clock.

Take, for example, a coach preliminarily requesting a TO if the Free throw shooter makes it. We grant it on the make. The clock did not start. We don't wait for him to ask again. So, why would we have to wait for a second request in the rebounding scenario.

If you don't wait for a second request in a live ball situation, that's up to you. But you still have to wait until B has gained possession before the TO can be granted. And you can't gain possession by rebounding a missed FT without the clock starting. The rule that I cited above says the clock starts as soon as the ball is touched. A touch always precedes possession.

The clock must start and stop.