In these situations what I usually see them do is tell the official on his sideline ahead of time that they're going to call timeout, so that he's ready for it. Then stand right next to him and say "timeout" before the snap. "T" signal? The ref isn't looking at him, he's looking at the players pre-snap, and I'm guessing they wouldn't appreciate coaches running onto the field and/or shoving hands into their line of sight right at the snap.
Also, there's no reason for him to tell the ref "I'm not going to call timeout". That's just stupid.