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

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

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

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

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

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