This is less "clean comic book fun," more "Old Testament horror." The only reason we know the Eye isn't God himself is that God clearly doesn't exist in the universe this comic takes place in. Instead of giving their "superhero" a weakness or flaw to make it relatable, the Eye's creators decided to go in the exact opposite direction and bestowed it with unlimited powers, including the frightening ability to penetrate men's minds.
Keen Detective Funnies Vol. 2 # 12, Page 49
"His third person speech annoying!"
Not only that, but it can also influence the minds of innocent people, apparently. Upon finding out that its sidekick, barrister Jack Barrister, was having problems with his wife, the Eye somehow persuades her to take him back.
Keen Detective Funnies Vol. 2 # 24
"Keen Detective Funnies: The Most Inaccurately Named Magazine in America!"
But don't worry, the Eye is a friend to all men who believe in justice -- the only thing it asks in return is your complete obedience.
Keen Detective Funnies Vol. 2, # 12, Page 54
The Eye was such a big hit, it seems, that soon other publishers rushed to cash in on the disembodied body part superhero craze. Another example is the Big Hand, an equally bizarre floating arm who communicates exclusively through cards written in blood.
Speed Comics # 12
"Meet me in the men's room. -TBH"