keep one's eyes off vs keep one's hands off

keep one's eyes off and keep one's hands off both are verbs.

Word	Noun	Adjective	Verb	Adverb
keep one's eyes off	No	No	Yes	No
keep one's hands off	No	No	Yes	No

As verbs, keep one's eyes off and keep one's hands off are synonyms defined as:

Other synonyms of keep one's eyes off include keep one's distance, stand back, stay away.

keep one's eyes off (verb)	keep one's hands off (verb)
stay clear of, avoid	stay clear of, avoid