....did a bit of googling:
To keep one's eyes peeled means to be alert, observant. This seems an odd phrase, but dates back to the 1820s in Britain, when Sir Robert Peel established the first organised police force. The officers were known as 'peelers, or 'bobbies'. They were expected to be particularly observant and to keep their eyes 'peeled', after their founder's orders! Of the two popular names, only 'bobby' survives.
And
It derives from an old verb pill, “to plunder”, which is the root of our modern word pillage. It came to us from the Latin root pilare, meaning “to take the hair off, pluck” (closely connected with our depilate), but which also had the figurative meaning of “plunder, cheat”, almost exactly the same as the figurative meaning of our modern verbs fleece or pluck. From about the 17th century on, pill was commonly spelt peel and took on the sense of “to remove or strip” in the weakened sense of removing an outer covering, such as a fruit. The figurative sense of keeping alert, by removing any covering of the eye that might impede vision, seems to have appeared in the US about 1850.
