I think you have it! Bingo! Yes, he went by the initials JT Blackwell on many records (Jesse Thomas), as well as Tom, Thomas, and Jesse. If our ancestors only knew what inconsistancy is doing for us genealogists. Ha.
I did see family write ups with "Jesse fought in Louisiana and Arkansas" but, haviing 3 grandpa Jesse's, I thought it was Jesse Thomas' father, who fought in the War of 1812. Later I found out that his 1812 fighting was more with the American Indians that the British stirred up to fight the Americans.
I am just so excited now!
Thanks a bunch, Gary!
Now I will know where to go from here.