I found out what it is.
nystagmus (a slight but very rapid jerking back-and-forth of the eyes)
It is a congenital defect in short haired, siamese type breeds. I was on a roll, trying to figure it out, and I finally did the right internet search.
It doesn't sound like it really affects their health, and he can still catch mice.
It is not a desirable quality, but old Theo is past making babies in this life. As long as he is helathy, that's all I care about.