PubMed Abstracts:

CONCLUSION: Homocysteine levels are dependent on Marsh classification and the regular use of B-vitamin supplements is effective in reduction of homocysteine levels in patients with celiac disease and should be considered in disease management.
Effect of B vitamin supplementation on plasma homocysteine levels in celiac disease. 
PMID: 19248194  Feb 2009

Results. Fifty-seven patients (88%) completed the trial. The tHcy level was baseline median 11.7 mumol/L (7.4 -23.0), significantly higher than in matched population controls (10.2 mumol/L (6.7-22.6) (P<0.01). Following vitamin supplementation, tHcy dropped a median of 34% (P<0.001), accompanied by significant improvement in well-being (P<0.01), notably Anxiety (P<0.05) and Depressed Mood (P<0.05) for patients with poor well-being. Conclusions. Adults with longstanding coeliac disease taking extra B vitamins for 6 months showed normalized tHcy and significant improvement in general well-being, suggesting that B vitamins should be considered in people advised to follow a gluten-free diet.
Clinical trial: B Vitamins improve health in coeliac patients living on a gluten-free diet.
PMID: 19154566 Jan 2009

Inadequate levels of pyridoxal phosphate in the brain cause neurological dysfunction, particularly epilepsy. There are several different mechanisms that lead to an increased requirement for pyridoxine and/or pyridoxal phosphate. These include: (i) inborn errors affecting the pathways of B(6) vitamer metabolism; (ii) inborn errors that lead to accumulation of small molecules that react with pyridoxal phosphate and inactivate it; (iii) drugs that react with pyridoxal phosphate; (iv) coeliac disease, which is thought to lead to malabsorption of B(6) vitamers; (v) renal dialysis, which leads to increased losses of B(6) vitamers from the circulation; (vi) drugs that affect the metabolism of B(6) vitamers; and (vii) inborn errors affecting specific pyridoxal phosphate-dependent enzymes.
B(6)-responsive disorders: A model of vitamin dependency.
PMID: 16763894 April 2006

Improvement of neurobehavioral disorders in children supplemented with magnesium-vitamin B6. I. Attention deficit hyperactivity disorders.
PMID: 16846100 Mar 2006

Moreover, there were such biochemical alterations as a decrease of magnesium level in the plasma and erythrocytes and a reduction of Mg(2+)-ATPase activity. The use of MAGNE-B6 allowed us to correct many of the disturbances.
[Neurological aspect of clinical symptoms, pathophysiology and correction in attention deficit hyperactivity disorder] PMID: 16548369 2006

Signs of mental depression are typical in adults presenting with coeliac disease. The results indicate a causal relationship between adult coeliac disease and concomitant depressive symptoms which seems to implicate metabolic effects from pyridoxine deficiency influencing central mechanisms regulating mood.
Reversal of psychopathology in adult coeliac disease with the aid of pyridoxine (vitamin B6). PMID: 6369511

But the two things which are relevant to CD are nutrition and immunity. People with CD have nutritional deficits because of malabsorption; common causes of neuropathy are B12 deficiency, B1 deficiency, B6 deficiency, and Vitamin E deficiency. Neuropathies are also commonly caused by the immune system through autoimmune mechanisims.
Celiac Disease and Peripheral Neuropathy, Norman Latov, MD, PHD 2002

CONCLUSION: This open study indicates that hyperexcitable children have low ERC-Mg with normal serum Mg(2+) values, and that Mg(2+)/vitamin B6 supplementation can restore normal ERC-Mg levels and improve their abnormal behavior.
Magnesium VitB6 intake reduces central nervous system hyperexcitabiliy in children.
PMID: 15466962  Oct 2004


These data provide a strong evidence for the occurrence of vitamin B6 deficienty in children with acute celiac disease.
Vitamin B6 nutriture of children with acute celiac disease, celiac disease in remission, and of children with normal duodenal mucosa.
       
PMID: 180789 July 1976
Personal Accounts of Pyridoxine Dependency and Seizures

http://www.angelfire.com/amiga2/jenniz/

http://www.epilepsy.com/stories/ps_1064252409.html

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On:  Pyroluria and B6/zinc deficiency