It looks like a piece broken off an ornate brass lamp or candelabra.
Anytime you are hunting a Civil War area, you have to remember there was a HUGE nostalgia for the Civil War that swept the nation in late 19th C.
There were gatherings and reunions of all sorts. Old soldiers wanted to go back to "where it all happened".
And a good campsite in 1865 was likely still a good campsite in 1890. So they brought all their creature comforts and lost the little bits and parts we keep finding mixed with war era relics.