After nerve damage to my inner ear some years back, I get nystagmus at times. The balance system is linked to the occular reflex, so if your balance goes wrong, eye movement can be affected. If I have a spell of vertigo, when it feels like the room is spinning, my eyes will move - a bit like when someone's just got off a fast roundabout.
A test used to diagnose inner ear malfunctions, the caloric test, induces nystagmus to see if the balance system works properly. I had that test, which was a wierd experience. One minute, fine, next minute, room spinning, eyes out of control. Sometimes I have to try hard to focus on things. It can be a drag. You do sort of get used to it after a while.