The little red self published booklet is a history written by descendants of Asa Peacock( 1790-1872) of N.C. and Indiana. It contains information from family tradition and not from records ,so it is not "verified" as "authentic".
The book by Lynett Hill has information taken without the knowlege of people who have other posts and websites that can be found on the internet. Since information posted on websites is considered public property, so to speak, anyone can use what information they find there and publish a book. The Hill book contains information from several different websites and posted histories so it should only be used as a guideline since some of those histories have not been absolutely verified and some of them are now known to contain errors. The best and most accurate information on the Peacock history can be found at the Peacock Association of the South whose historian is very careful not to claim something as absolutely accurate without documentation to back it up. He does speculate and give "best guesses" and "circumstantial evidence" but always acknowleges and explains his reasoning for those things for which he does not have "verification". His name is John J Pierce and he has published a large hardcover book on the line of Levi Peacock (1756-1822) who was born in Wayne County N.C. and died in Wilkinson County Ga. The origin of Levi Peacock of Pierce's book is the same as many if not most of the Peacocks who now have descendants in the Southern and Western states and even some in Northern and Midwestern and Mideastern states. Mr. Pierce and the Peacock Family Association of the South have much data and information and documentation of other lines who are related to the Levi Peacock line as well as data for lines that have not been established as having originated with the Peacocks who were in N.C. as early as 1720.
Perhaps this will help in your search for Peacock documentation.