The person you are calling Thomas W. Pickle must be the person I am calling Thomas Newton Pickle. I don't see why he could not have had four names, as it seems this practice was somewhat common in Bedford County, Tennessee, particularly where a middle name is a non-family name (like Washington or Franklin or Jefferson, or more "locally famous" names, like Cooper, Tillman, Newton, etc. (and in many cases it is a combination of these two types)).
Thomas Newton Pickle was born abotu 1874, and married Mary Catherine Stephenson (who also married William Bowden Moss and John Primrose). This Thomas Newton Pickle was the son of Squire Daniel Pickle, and his wife, Josephine C. Swiney.
The 1880 census of Bedford County, Tennessee gives Thomas as son in the household of Daniel Pickle. Notice that Thomas has a sister named Lottie, among others.
Josephine C. Swiney was the sister to Squire Daniel Pickle's father's 2nd wife.
I think you can find other mentions of Thomas on this forum by searching for "Newton". There were at least a few Thomas Newton Pickles.
So can you post your new information here, so we can all benefit from it? :)