That it is a variant of peep is seen in the child's word peek-a-boo, equivalent to bo-peep.

But along about this time we began to get so many complaints about our dry salt meats that I decided to have a little peek at our stock for myself, and check up the new cellar boss.

Once he lookednot exactly looked; perhaps peeked is the better word; took just the tiniest lightning peek out of the tail of his eye, and found a smile waiting for him.