Ok maybe I was wrong and giant eyeballs that are on fire
CAN have hands. I mean, if they really want to and that's how it was in the movies anyway.
Seriously, people. "The Eye" as Sauron is because of a lot of reasons that don't have anything to do with him actually being a giant flaming eye. Was The Mouth of Sauron really a giant set of lips and teeth? Maybe he was very drippy instead of being on fire. You know, from the drool. Or maybe he drooled fire! That would be so cool.
"The Eye" would find you because that is the part of Sauron that Sauron was looking for you. When you got close enough "The Nose" would smell you. Then maybe The Hand would grab The Sword and Stab You.
The Eye of burrahobbit is on you. burrahobbit isn't a giant eyeball. It's a metaphor.