It certainly is possible to have neurological symptoms from gluten sensitivity/celiac even in the absence of gastric symptoms. These can include peripheral neuropathy, cerebellar ataxia, even brain "lesions" resulting from the autoimmunity process.

There are certainly other possibilities (including Lyme, which is a great mimicker of other conditions), but it sounds like she at least needs some initial blood testing for cleiac/gluten sensitivity--the anti-gliadin IgG and IgA assays, total IgA (if total IgA levels are low, the other test results can be skewed), anti-transglutaminase IgA/IgG, and perhaps anti-endomyesial assays, just to see if something shows.

The gold standard for diagnosing celiac is still villious atrophy upon small intestinal biopsy, but there are certainly people who are gluten sensitive with all sorts of neurological symptoms who don't show that.

It would be a good idea if you look at the Useful Websites heading here, especially at the massive database of info and studies known as The Gluten File, put together by jccglutenfree and the most comprehensive info source on the subject yet devised; it would help bring you up to speed, get you familiar with the reseach, and help in forming questions--note well that most doctors are not anywhere near as well-versed in this area as jcc is.