Yes, I think that your "Luke L. Brumley of the 11th Texas Cavalry" was the same "Luke L. Brumley, b-1839" that was mentioned twice in my book. One bit (approach) of indirect evidence is to look at the other members of these 1861 Clay and Cooke County Texas militia members who joined the 11th Texas Cavalry. ... Several are listed in the 11th Texas Cavalry.
I find it interesting that your "Luke L. Brumley" was found in the general "11th Texas Cavalry" listing of the "Sailors and Soldiers System" then I could not find his company. Maybe I don't know how to use the software, but I've spent so much time studying fragmented records, I sorta shrugg this as being fragmented data.
Chances are good that your "Luke L. Brumley, b-1839" was a young militia member of the Clay and Cooke County 1861 militias. After years of working with family data, I know that we have to wait until we receive data from the Luke L. Brumley's family.
What I think doesn't matter. The historical record matters. We are trying to persuade readers to critically study the original records.
Do you believe this is the same "Luke L. Brumley" that also served with 11 Texas Cavalry as given in my original message?