I've only just read that Dr Alessio Fasano, world leading expert on all things celiac and gluten, says that neurological symptoms like brain fog are seen in around a third of gluten sensitives, more than in celiac disease. Depression and anxiety also are seen more often with gs than celiac.
I found that my brain fog went after going g free. I was never sure if it was a coincidence. Seems not, so another great reason to try going g free, having first ruled out celiac of course.
(Report of this comes from Jane Andrews talking to dr AF in Very Well, Aug 2016)