This is a big deal! I’ve had Ataxia (SCA unknown) for 23 yrs. One of my first symptoms was double vision after walking the beach for 2 miles. The symptom continued while I was being diagnosed and then for some reason disappeared for many years. Recently it came back strong lasting several hours only in the morning. By accident, one afternoon it hit me strong after downing a very sweet coffee drink. I was able to look back at what was occurring for me when it often occurred in years past and concluded that “stress” (no surprise) and “blood sugar spikes” were the likely cause. Blood sugar spikes occurred with morning coffee with sugar and would last several hours. I often didn’t eat during this time or drink water. All of this from a single 1/2 cup of coffee. I have tested my theory for the past 6 weeks, cutting my sugar intake daily from all foods to just 45 grams. Double vision immediately stopped and overall my stamina increased dramatically contributing to better walking. My nstagmus/vertigo is still there off and on but increased stamina really helps walking. I’ve had only one incidence of morning double vision after a very difficult night of indigestion and poor sleep but it didn’t last hours as before. Recently saw both my Endocrinologist and Primary dr who say this is unusual but can happen. My primary dr even explained how blood glucose affects the lens in the eye. Blood tests show I do not have diabetes and blood glucose levels are good. I don’t know if limiting dietary sugar will help any of you but trying it can’t hurt. My theory for me is that long term reduction in sugar and avoiding sugar spikes may affect other eye symptoms, and if lucky, vertigo. 
That’s wonderful news…sugar can be at the root of some of my problems too. Nothing specific like you found but…I do notice ataxia symptoms can vary if I consume too much sugar…it could be coincidental…I don’t know for sure.
I also have chronic eye problems…I’ve had treatment from a NeuroOpthalmologist
I went to a neuro-opthamalogist specifically for double vision (Harvard trained) and he told me this was just something that was part of my ataxia—no treatment other than prisms but this was sporadic so prisms won’t work. I’m starting to read about diabetic eye disease as apparently I’m unusually sensitive. Just had bloodwork to check for diabetes and I’m normal. Since this has occurred for 23 years it must be an aspect of Ataxia not yet studied.
interesting info related to blood sugar and double vision:
Acute Hypoglycemia Decreases Central Retinal Function in the Human Eye - PMC.
also Ataxia:
Cerebellar Ataxia and Hypoglycemia:
This disorder may occur in patients with altered cerebellar glucose kinetics. In the case reported above, we present a diabetic with prolonged and severe cerebellar ataxia after an episode of severe hypoglycemia.
Prolonged Cerebellar Ataxia: An Unusual Complication of Hypoglycemia - PMC.
All of this is connected to people with diabetes. I don’t have diabetes. Just had tests to check. Also my experience is Hyperglycemia (blood sugar spike) from what I can tell —but who knows, maybe hypoglycemia follows shortly after causing double vision. All new info to me.
Definitely food for for thought. But…on reading the link to one patient…his previous history would suggest a link to Acquired Ataxia…
‘His medical history included active polysubstance abuse (benzodiazepines, alcohol, cocaine, and tobacco), schizophrenia, hepatitis C, hypertension, and myeloid leukemia in remission’
My own ‘double vision’ and nystagmus….appeared when I had Iritis (a serious eye condition). This could have been coincidental…I was experiencing increased Vestibular symptoms several years before a diagnosis of Cerebellar Ataxia.
I still don’t have a link with a specific type or cause…but my Neurologist suspects it might be Recessive because some ‘symptoms’ appeared in childhood.