Even if it had a rigorous and testable definition it would still be suspect by virtue of us having searched for evidence of it under the guise of science.

To explain it by analogy, we had the concept of women and men for at least thousands of years. Socially construed by physical appearance and behavior. Then in 1905 Nettie Stevens discovered sex chromosomes. Her discovery "found" the existence of men in women in the epistemological universe of science. But then a curious thing happened, people began placing people in social categories based on sex chromosomes. It's an incestuous loop of logic that hoists itself into validity simply because folks forget how it occurred.

If we went searching for a scientifically rigorous definition of "thinking" we would forget we made the same fatal leap of logic.