All I have regarding John Moore, the brother of Joseph, is from the Caswell County, NC Will Books 1777-1814, 1784 Tax List, Guardian Accounts (By Katharine Kerr Kendall):
"John Moore, will 20 Sept 1776, son Joseph, heir at law, Nancy & Sarah Moore, daughters of Joseph; son John; grandson John, son of John; grandson (not christened but called) Patrick Henry Moore, son of John; daughter Sarah
McGehee; grandson John Moore McGehee; daughter Elizabeth Shoemaker and her children; daughter Frances Stewart; grandson John Moore Stewart. Land on Cain Creek to be sold. Son Joseph Moore, heir at law and second son John Moore, son in law, Montford McGehee and Archibald Murphey to execute will. Wit: Abm. Rice, Anne Rice, Mary Allen."
John Moore's son John passed away about 1784 leaving some children under the age of 18 which included my great great great grandfather William Cocke Moore who moved to Tennessee, Alabama, and lastly to Tishomingo, Co., MS.
The elder John Moore may have been the son of a Joseph Moore perhaps of Lunenburg Co., VA. I could not confirm this information as of date.