What are the proper geographical boundaries of the American South?

One could certainly say that Southernish influences exist beyond any orthodox boundary definition. California, a Union state during the Civil War, had lots of Confederate sympathizers with roots in Dixie in Southern California, to cite just one of many examples. Parts of Ohio are basically Southern for another.

https://upload.wikimedia.org/wikipedia/commons/thumb/3/34/Dixie_states_map.svg/800px-Dixie_states_map.svg.png

Dark red indicates the states almost always included in modern-day definitions of Dixie, red – sometimes included (see Southern United States for the U.S. Census definition), while pale red – occasionally included due to their historic connections to the South.