Ideas, especially engineering ones, are quite the brain product.

That does not need much fuel. Seriously, are you never got ideas? They just appear in your mind without any effort at all.

Tesla and Leonardo didn't do all the stuff, they got idea, beg for money and pay them to those who did all hardcore engineering job with all calculations and specific knowledge to implement them. Tesla didn't do strength analisys and architect calculations to buld f.e. Wardenclyffe Tower. He just ordered it.

And so on.

Art is also not a kind of thinking intensive task. You need talent for that, not brain power. Similar to ideas. Good artist don't think a lot over his creation. It is usually bad artists who are trying to replace lack of talent with hard thinking and so use brain a lot.