Put a little more generically.
Once the game has started, anyone can be granted a timeout whenever the ball is dead as long is it not a successive timeout after time has expired in the 4th Q. or OT.
Only when the ball is live are there restrictions on who can call timeout....only the team that has a player control (not team control).
Between FTs, the ball is dead.
If it's not dead, it should be shot to make sure it's dead.