Nystagmus Support Group
Nystagmus is rapid involuntary rhythmic eye movement, with the eyes moving quickly in one direction (quick phase), and then slowly in the other (slow phase). Nystagmus is a relatively common clinical condition, affecting one in every 5,000 to 10,000 individuals. Nystagmus generally causes a degree of vision impairment, although the severity of such impairment varies...

Gabapentin made me miserable.
I dont always care for alcohol so can't say if it helps or not.
Give it a try and have a good friend or family member pay close attention to see what it takes to slow down and eventually completely stop the nystagmus. As you are not a drinker, I would advise that don't try to rush this experiment. I drank for many years around close friends before it was even noticed. A dear lady friend noticed it while our group was at the neighborhood bar. She was astounded, as was I. We decided then that we would experiment, to see how much it took for the effect. Turned out to be a 6 pack. Depending on the speed of consumption. Please let us know about your results. I intend to contact Dr Lubnowski, Professor of Ophthalmology at Washington University in St Louis, and discuss this with him.