One of the criticisms the anatomists of the Renaissance faced was that their conclusions were anti-Aristotelian.
I think the fact that you can get knocked out with a moderate blunt force trauma would be the big clue. No other part of the body can make you unconscious because it gets jarred really hard, can it?
Rumor has it, guys think with their penis. Especially when attractive women are nearby. 
It probably didn’t take long to observe the brain in butchered animals. Pig brains are still eaten with eggs today.
Maybe, after a battle a dead guys smashed skull revealed his brain is very similar to many animals.
Eventually they made the connection.
Forgive me, but what you’re saying only seems to make sense if they noted that the brains of various animals were “thinky”. But all you seem to be saying is that people noted that the brains of various animals were “delicious”; and I don’t see that making that connection would be much help at all.
The observation that human skulls contained the same organ as animals.
Could have lead to the understanding that it controlled thinking and body movements.
Animals can be quite cunning and so can humans.
I don’t know when early people made that connection.
Ancient Skulls showing signs of successful surgery have been found.
Early people were familiar with the brain and body movement. I’m not sure if these societies understood how thought takes place.
https://www.google.com/amp/s/relay.nationalgeographic.com/proxy/distribution/public/amp/2016/06/what-is-trepanation-skull-surgery-peru-inca-archaeology-science
If you don’t know whether it’s the brain or the heart that does the thinking, how does examining another animal help?
Well, with ancient skull surgery. Weren’t they crudely treating seizures and spasms?
Making the connection between the brain and body movement.
Animals also had hearts. I don’t think any conclusion can be made simply by seeing that animals have similar organs as humans. IIRC, ancient Egyptians considered the brain to be where mucous was produced. That kind of makes sense; it leaks out of your nose.
Initially it was to release extreme pressure due to brain swelling caused by trauma. One doesn’t need to know the brain does the thinking to associate blunt trauma with swelling and an intensely painful build up of pressure.
There are so many trepanated skulls from Neolithic times (up to 10% of all known skulls) that I think it’s likely that at least some of them were done as part of rituals and had nothing to do with health care. But in any case, even if trepanation were done to treat seizures, it doesn’t imply people knew the brain was responsible for thinking. It just means they thought the brain (or maybe the skull) was associated with seizures. When you have a high fever and your skin gets warm, your thinking can be disordered too, but it doesn’t mean the skin is responsible for thinking. And I’m still not seeing what clues animal brains supposedly provided.
Well, you could do experiments with animals: Damage but don’t destroy an animal’s brain, and see in what way it’s impaired. But I don’t think that experimentation has been systematic enough for that for more than a few centuries.
The chest. Hit someone hard enough in the chest, and you’ll “knock the wind out of them”.
nm