Mentone has been hunted a lot over the years. But there should still be some goodies. If you go a bit north of Mentone, there is a road called Yankee road. The Yanks built that road, and to do so they would have had to have camped nearby. That might be worth your looking into. Be sure to let us know how you do.
Mentone is a beautiful old place! I'm from Guntersville and have spent some time up there at a cabin upstream of that swimming hole......I would love to go into that swimming hole with scuba gear...Let us know what you find!
Read your regimental histories. It is all available on the web. I found a lot of relics in Bridgeport , Scottsboro many years ago but stay away from the TVA boundaries and have written permission from a land owner. There were tens of thousands of soldiers down there during the Winter of 1863-64 ... and all of the relics will never be found. There are still pockets of relics there