In my experience, any time Not The Head Coach is authorized to call a time out, it's because the HC has delegated one side of the ball to assistant coaches. For example, the HC calls plays on offense, then lets the defensive coordinator take over when they don't have the ball. The HC is then busy looking at film/talking to the QB when they're on defense. In that situation, there's only ever one "active" coach that can/will call a timeout.
If they ever try to designate multiple coaches/players/water boys, then I'm just going to grant any request for "Timeout" that I hear behind me -- and if that means the HC is HACKED off for using a time out when he didn't want to, well, that's his problem for not controlling his sideline. That's not "by the book" legal, but it's a good way for the coach to understand the rule in a very "malicious compliance" manner.