"vanish, abscond," 1920s, American English, probably from mid-19c. notion of disappearing south to Mexico or Texas to escape pursuit or responsibility, reinforced by Native American belief (attested in colonial writing mid-18c.) that the soul journeys south after death.
Idioms and Phrases with go south
Deteriorate or decline, as in The stock market is headed south again. This expression is generally thought to allude to compasses and two-dimensional maps where north is up and south is down. However, among some Native Americans, the term was a euphemism for dying, and possibly this sense led to the present usage. [Slang; first half of 1900s] Also see go west.