This archetype is almost always a side character or one that pushes the plot forward like the wise man in the heroes journey. This makes them a very flat character. This character though can be powerful. This came to me mostly because of my brother. He is the kind of person that is quiet and watches then when he has something to say he speaks up. Everyone is floored by his wisdom and pays attention because his words are used sparingly. My first hero in my first series was like this. He had studied as a social worker and watched rather than acted. When he did act it was to the point and was effective. No extra moves and no showing off. This character works as it shows power while giving a female character more space to shine in a novel.
It wasn't easy to find this character as a main character at all. Like I said they are often relegated to the side. But Death is probably the best example of an observer or watcher archetype. He doesn't want to be drawn into life as that isn't where he belongs. Ironically he is the most fair and reasonable aspect of Discworld. He is consistent and just while the rest of the characters are anything but what is expected. The wise wizards are all fools and the witches are kind.
Like the loner Achetype the observer often keeps himself apart. The difference is that they are inherently part of the system. Death can't keep himself apart from humans as he is an essential part of their lives. Perfectly highlighted when Death goes on vacation.
The thing with the Observer is that at first no one thinks they have anything of importance to say. Even Mort didn't think much of him at first. It is only over time as he reveals that he has gained wisdom from being an Observer.
I think his modern incarnations are better examples of him being an Observer though his earlier escapades have him as the true Observer. So this is more about him over his whole incarnation. As a time traveller he has the opportunity to watch everyone. It is only later that he actively changes things for people. Mostly he lets the situation guide him and then is surprised that he had any effect at all.
One thing that shows off that he is the Observer, like Sherlock, is that we aren't privy to his thought process. We then become the Observer. I do wish they would give Dr Who an arc where he truly finds his/her equal. Someone they could grow old with and finally close their arc. They've done other arcs that could have achieved this but in the end because of ratings they have dragged him past where he should have come to a rest.
Buffy the Vampire Slayer
Angel from this series starts off as the Observer and he often falls back into this archetype. I think this is a bit of what Edward was supposed to be in Twilight but ended up just being creepy. Angel could also be considered a loner as well. I have said these have done it well but I really do think this trope could be done better. That we can have someone who is a true observer, someone willing to let the other characters have space but also holds a significant role in the story as a whole.
The reason I like the Observer trope is that often the character relegated to bit parts and supporting roles in stories are done very blandly and two dimensional. Taking a two dimensional character and fleshing them out can be interesting and unique.