I don't kfl, I think it's pretty common to use the phrase 'keeping an eye open' or 'keeping an eye on' to indicate a slightly attenuated degree of attention to a subject or object. Using the phrase 'keeping my eyes (on, open)...' would indicate a more single-minded and complete attention.
This may just be rumor or Hollywood lore, but I'm pretty sure I remember somthing about Peter only having one eye. If I'm not mistaken, his right eye was removed at a very early age. I assume Peter has made this part of his character.
(Wow! Two posts in one day! I don't usually post this much in a year!)