Working as a nanny I've sometimes found -- especially with older children (6+) -- that the time-out works best when it is for me! So what I say to the child is, "I really don't like how you're behaving right now and it's making me upset so I need to take some time by myself to cool-down." and then I go away and sit quietly in another room for a bit. So without "punishing" the child I'm able to show that there are consequences for their actions and also that sometimes it's good to remove yourself from a situation in order to recenter.
I do take a time out (can I have one for my age, pretty please, I have stuff to read…. ) when I am grumpy or spiraling. I think it is great to model taking a break when you need one.
If one of the kids is grumpy, I expect them to leave if it their behavior that is inappropriate. I am not going to be pushed out of a room or whatever when I am not the one who is engaging in (typically unrelenting) behavior.
So - I don't really love parents taking time -outs in lieu of children (unless they really need one as they themselves are grumpy), as I don't think it teaches kids that certain types of behavior is not okay.