Of course, there won't be a precise known answer to the question, as it is not even known precisely what percentage of the genome is functional in the first place - but I am still looking for research.
The book "Principles of Neural Design" claims that "20% of our genome is devoted to coding neural signaling molecules". This seems not only vague, but also suspect to me, as that is more than the fraction of DNA that is known to have a function in the first place - maybe they meant only protein-coding genes?
One hears a lot about the human brain as "the most complicated object in the universe" etc., but I would like to put a number of that and compare the genetic complexity needed to express it to that needed for other body parts.