Danny, I came across this Cook Family when I was trying to find information on Charles Alton Cook, son of James John Elmore Cook and Belven Lockwood Daniel.
I have a Jasper James Cook born December 20, 1840 Alabama and died January 8, 1910.According to the Widow's Pension Application regarding James Jasper Cook(name turned around) of your grandmother Mary Livingston Cook, she states James Jasper Cook was in the 41st Mississippi Infantry Regiment, Co "G" and died January 8, 1910.
However, there is a Jasper J. Cook in the Iron Bluff Cemetary, Lone Star (Morris County), with the same vital information, "but", this man's Civil War Service shows a Texas Cavalry info.Maybe someone at www.findagrave.com, made an error?Don't know, but it is interesting.
Iron Bluff Cemetary is where I found John Elmore Cook born 17 November 1869 MS and died 04 Feb 1953, Morris County, TX. John Elmore Cook is a son of Jasper Cook and Mary Livingston.At first I was given the name, James John Elmore Cook, or James Elmore Cook, but after finding his death certificate on www.familysearch.org., his name is "John Elmore Cook".
I also found your grandmother, Mary (Livingston)Cook's death certificate on the website, www.familysearch.org, born August 22, 1845 Alabama and died February 1, 1924. On her death certificate it lists "Clark" Cemetary, Morris County TX. I went on www.findagrave.com and she was not listed in that cemetary.There are lots of questions.
Danny, if you give me your email address, I will connect to my tree on www.ancestry.com and you can go from there, I have gotten alot of information.