I think 'eye movement changes' is fine as part of a descriptive title. In that case, 'eye movement' acts as a compound adjective to modify the noun 'changes'.
I have found at least one other paper in a respected journal that uses this, the full title of which is:
Saccadic eye movement changes in Parkinson's disease dementia and dementia with Lewy bodies
As for the body of your text, you'd have to consider what is most pleasant to read and what the style-guide (if there is any) says. I personally think the shorter version (same as in the title) is better because an alternative phrasing tends to be overly verbose.
As for the grammatical number, I'd go with the singular. Since you're using a compound adjective on a plural noun, the result is already plural.
If there is a specific reason you think you need the plural, an example of which could be (and I'm making this up) that there are two types of eye movements, up-down and left-right, and you consider both, you might want to convey that to readers differently. For example, if this example were not made up and this is an actual thing, then there would be a technical term for it which your readership would understand. In that case, you should use the adjective-form of that term because it's clear to your readership.
If there is no specific reason for needing the plural, the singular should suffice.