A person who says and does mind-numbingly dumb things. At a glance, these words and actions causes one to roll their eyes.
When talking to an eye dropper, one often stops paying attention to them to continue with matters more important.
More important matters include but are not limited to, staring off into space, looking at the floor, listening to someone else's conversation, talking to a cat with your mind, etc.
One occasionally comes back to the eye dropper to say something along the lines of "Oh yeah?" "That's nice" "That's bullshit" "Some don't get it". This is only done to remind them that there is someone else in the room. Accidentally listening to an eyedropper speech can result in lost IQ points.
One can spot an eye dropper talking to themselves while standing near others or on facebook/twitter, buying their pets clothes.
An eye dropper is a step down from a "Fuckwit