We're all on the same page, that's good.

I was quite impressed by the mutants in the Metro 2033 game. They actually behave like animals in most situations and don't all immediately beeline to you and bit until they are dead.

There's big rodents that silently dart out of their holes while you're not looking to bite you in the legs and immediately run away when they get hit.

There's wof-hyena things that often sit on heaps of rubble as sentries that will call the whole pack to them when they spot you. You frequently encounter packs running through open spaces and when they have been spooked by larger predators they will just run right past you.

And big gorilla mutants that try to intimmidate you but won't attack while you're looking at them.

And then there's giant spiders that can't stand exposure to bright light.

Hard to do these things in something like D&D, but I think in Fate or Apocalypse World it should work reasonably well. I think the general idea is beasts that threaten to attack you but won't do so until specific circumstances are met. And they have to be dangerous enough so that you really don't want to fight them. Being safe while looking at a creature seems easy enough, but what if you want to climb a ladder or clear the rubble blocking a door? Then you have to start thinking of alternative approaches. There's a lot of exciting play with trying out methods to distract or chase them away without making them attack. Or you could simply wait for them to move on while you're already under some time restriction.

But I think the basic concept of "monster that won't attack until you set it off" should work in any game.