Which organ did the Aztecs and the Greeks both wrongly identify as the seat of thought?

The heart. Aristotle placed intellect and sensation there and treated the brain as a cooling device for the blood - a radiator. The Egyptians agreed enough to preserve the heart carefully during mummification and pull the brain out through the nose and throw it away.

It was not stupidity. The heart visibly responds to fear, love and exertion; the brain does nothing you can feel. Hippocratic writers and later Galen argued for the brain from evidence - head injuries change speech and personality, the nerves converge there - but the heart view had Aristotle's authority and survived for centuries, and it is still in the language: learn by heart, heartfelt, take it to heart.

The idea has had a curious partial rehabilitation. The heart has a substantial network of its own neurons, and signals from it influence attention and emotional processing measurably, which is a real finding regularly overstated into claims about the heart thinking. The Aztec practice of removing a still-beating heart in sacrifice belongs to a different logic again - the sun was held to require it - rather than to a theory of where thought happens.