I wouldn't have thought that there was any particular origin. "Peel" means "uncover" - as with an orange, a banana, or ourselves when we peel off our clothers - so the phrase simply means "keep your eyes uncovered".
The phrase first appeared in print in the USA in the St Louis 'Daily Morning Herald' in 1853. It took the form of a piece of advice..."Young man! Keep your eye peeled when you are after the women." As another answer has already suggested, it clearly means 'open'.