With your lead I found the following in 1900 Census in Alamance Co., Graham Township, NC
Blackmon, William Head b. Nov 1870 Lydiawife b. Apr 1873 Arthursonb. May 1896 William D. sonb. May 1898 Paulsonb. Mar 1900 Shoe, Tempie Mother-in-law b. Jan 1846 Shoe, NancySister-in-law b. Sept 1882
Lydia's mother Tempie and sister Nancy living with Lydia's family.This means Peter was either dead or had left by that time and that he and Lydia had another daughter, Nancy in 1882.
According to my living aunt Ruby,Lydia and Nancy were the sisters of James Wilbert who attended his funeral in 1937.
For me this number of facts, even lacking birth, death or other documents, tells me that I finally have my great grandfather identified.Thank you so much.Of course, I am very interested in the other info you have and will be glad to provide any info I have that you would need.