Is gothic country a genre of country music or a genre of post-punk? Yes.
Gothic country is inescapably tied to both genres, and it's hard to place it neatly among either country music or gothic rock, as much as progressive metal is too metal to fit in neatly alongside prog rock bands and too prog to fit in neatly alongside metal, and neofolk is simultaneously too industrial and electronic to fit in neatly in the folk genre and too acoustic and folky to fit into industrial easily.
Slim Cessna's Auto Club prefer to call themselves a rock band, and there's no easy way to categorize their apocalyptic hillbilly music that draws from bluegrass, folk, early country, gospel, klezmer and post-punk, songs that are about despair, loneliness, misery, the end of days, murder and the devil. Cinematic music that paints a portrait of rural Americana for which God has abandoned its people long ago and redemption is unlikely.
The band weaves in elements of Morricone Western scores, honky tonk era country, and the doom perspective of
Black Sabbath, making twangy cowgoth that defies conventional categorization. They're sort of a cross between the country gospel of
16 Horsepower that's more focused on the damnation side of religion than celebrating the Lord's glory, and the Gothic country of the
Legendary Shack Shakers, painting a grim, brimstone imbued portrait of the American South.