New Scientist is generally ok, I find. The studies that article mentions also rely on the assumption that gendered behaviour is innate, which is also a vital assumption for TRAs. As FlippyKing says, silly idea. Gina Rippon, professor of cognitive neuroimaging, has written an accessible book, Gender and Our Brains, which explores this area. I haven't read it yet, but it's likely to be more up to date and less palatable than that article to your TIM. Here's a review.

Contrary to what early coverage of brain imaging technology claimed, neuroscientists no longer believe that specific types of activities and aptitudes are dealt with solely in discrete parts of the brain. Instead, the brain is a network of networks. It is also extremely “plastic,” constantly changing to reflect whatever its owner experiences and does...It makes no sense, Rippon argues, to speak of brains as fixed organs when they can be changed literally at will.

Much of the rest of Gender and Our Brains describes how exquisitely sensitive to social input the brain is—especially in infancy and childhood—and how pervasively gendered that input is. “A gendered world will produce a gendered brain,” she writes.