I'm not sure I follow you. Why would you need to analyse "thinking" in order to "get a start on building AI"?

Becuase thought is essential to intelligence. Why would you need to analyse intelligence to get a start on building artificial intelliigence? Because you would have no idea what you were tryinng to do if you didn't.

Presumably it's enough to systematize the various computational algorithms that lead to the behavioural/functional outputs associated with intelligent thought.

I fail to see how that is not just a long winded way of saying "analysing thought"