I really think you need to look at that Benton / Carroll Co TN area - say 1850 and 1860 census records, etc.

I found a William J. Thompson from Carroll Co TN in the 7th Tn CAV USA who died 1864 at Andersonville prison, also a John C. Roach in the 6th TN USA who died as did a William H Roach in the 12th CSA who died....and a Chesley P Thompson who died 1861 in the 22nd CSA. All of these are Carroll Co - but as I said, this group was on both sides of the line between Carroll and Benton Co TN.

I know Benjamin Thompson is in the 1850 Benton Co TN census, but I cannot find that now.....

for the 7th TN CAV USA (in which my James Mullins was)
I found:
John C. Thompson
John W Roach - Co K
George W and James Thompson - Co K
Calvin L and William J Thompson - Co M
and from Benton Co TN in 7th CAV USA
James H. Barnes CoCo C
Frederick B Barnes CoCo I

a heads up on this group - in 1850s some from these families (Kilbreath, Norwood, Malone, etc.) went to Illinois, and those men were captured about the same time as the ones from 7th TN CAV USA and they all ended up in Andersonville prison where many of them died. The survivors - many ended up in 1870s moving to Arkansas.

Mary