The most common and most likely answer to this crossword clue is the 9 letter word NYSTAGMUS
I've seen this crossword clue in The Guardian
N
Y
S
T
A
G
M
U
S
More clues leading to the result NYSTAGMUS
Buddy explains!

The straight part
We know that "eye movements" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case eye movements = nystagmus.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does NYSTAGMUS mean?
NYSTAGMUS noun- Rapid involuntary eye movement, usually lateral