I read a definition of the word “squint” in Merriam Webster Dictionaries which was:
of the eyes : not having the visual axes parallel : CROSSED
“Crossed” (or cross-eyed) is in fact a type of a pathological condition relating to eye known as Strabismus or squint-eyed. So I don’t think it should really be there as the equivalent of the definition because it is a type of the squint-eyed disease which is broader term and the type is specific.
Strabismus is the medical term for a permanent misalignment. Strabismus is derived from the Greek for squint.
But, looking down your nose causes the eyes to misalign temporarily. This is also referred to as cross-eyed, or having your eyes crossed.
Squinting is layman’s term and hence encompasses more than one phenomenon: Closing one’s eyes to get a better view, looking askance, etc.
Just for completeness, saccades are movements of the eye horizontally between fixed points. Nystagmus is a twitching type of involuntary saccade usually due to neurological or extra-occular muscle issues.