The authors "found that the PON1 genotype and hearing nerve agent alarms were independent and the findings robust to both measured and unmeasured confounding, supporting a mechanistic [gene–environment] interaction. ... Moreover, the change in the combined effect from one category to the next was significantly greater than the sum of the independent effects of the environmental exposure and the genotype". Although organophosphate pesticides could have triggered the nerve agent alarms in use at the time and contributed to neurotoxic symptoms similar to GWI, Haley et al. ruled out pesticides as a primary cause of GWI, citing that pesticide use was "ubiquitous long before the approximately 10,000 alarms began sounding at the start of the air campaign when Coalition bombing of Iraqi chemical weapon facilities released the fallout cloud that reached U.S. troop concentrations just as sarin was detected at multiple sites," while "the PON1 R isoenzyme is the more efficient detoxifier of most pesticides." Less likely causes
According to the VAs 2008 RAC report, "For several Gulf War exposures, an association with Gulf War illness cannot be ruled out. These include low-level exposure to nerve agents, close proximity to oil well fires, receipt of multiple vaccines, and effects of combinations of Gulf War exposures."
Skew deviation is an unusual ocular deviation (strabismus), wherein the eyes move upward (hypertropia) in opposite directions. Skew deviation is caused by abnormal prenuclear vestibular input to the ocular motor nuclei, most commonly due to brainstem or cerebellar stroke. Other causes include multiple sclerosis and head trauma. Skew deviation is usually characterized by torticollis (head tilting) and binocular torsion. The exact pathophysiology of skew deviation remains incompletely understood. Skew deviation appears to be a perturbation of the ocular tilt reaction, which is itself is most likely a vestigial righting response used to keep fish and other lateral-eyed animals properly oriented.There are three types of skew deviations:Type 1: Upward deviation of both eyes; sound-induced vestibular symptoms; both eyes show counterclockwise rotary upward rotation
Type 2: Hypertropia in one eye; dorsolateral medullary infarctions; excyclotropia in the ipsilateral eye; hypertropia in the contralateral eye
Type 3: Simultaneous hypertropia one eye and hypotropia in the other eye; upper brainstem lesion

References
Further reading
Adams, Raymond D.; Victor, Maurice; Ropper, Allan H. (1997). Principles of Neurology (6 ed.). New York: McGraw Hill, Health Professions Division. ISBN 978-0-07-067439-4.