"The Girl I Left in Sunny Tennessee" (aka, The Girl I Loved ...) was composed by Harry Braisted and Stanley Carter in 1899. See Traditional Ballad Index. There are a number of folk and cover versions by Poole, Stoneman, Mainer and others and versions appear in Randolph, Wolf and others.

It is not clear that this is the song Topical Tom is looking for, since I have seen mention of a song with his exact title.

Also see "My Sunny Old Tennessee Home," Albert B. Wilson, 1882; sheet music at American Memory.