I've never heard "drop an eye." Similar phrases with the meaning "take a look" are "run an eye (over something)" or "cast an eye (over something)"

I think you're wrong there. I've never heard of "drop an eye" in English. You can say "Please run your eye over this page", meaning please check this page for errors, or relevance. You can say "He dropped his gaze" or "he lowered his eyes" meaning he looked down so as not to stare straight ahead (usually at someone). Hope that helps.

you're right. it means take a look.

Are you thinking of 'drop your eyes'? If someone drops their eyes it means that they look downwards.

Well, nothing is academic I guess, but a lot of folks are using "drop an eye on" to mean: Observe or take a look Thank you all for the help