It's not about Baekje and Silla.
This country had been united for 1500 years after the conflict between Silla and Baekje.
Doesn't mean cultural and identity differences don't persist.
Narrowly, in 1963. It voted against him in subsequent elections. Polarization was quite evident in the 1971 election, well before Gwangju (and, though Jeolla was not yet an anti-Park stronghold in 1967, the east-west polarization was already quite obvious).
Also, 1963 looks highly unlike later elections and came at a time when democracy was far from mature in South Korea and when rural areas in general had few qualms with a strongman as a leader (while Seoul was less comfortable). The 1963-1967-1971 evolution is interesting as a source of insight into modern elections, but it hardly disproves the notion that the polarization of Korean politics is of recent origin. Rather, it suggests that, as the country settled into early democracy, identity politics asserted themselves quite boldly. Gwangju certainly crystallized support for the democrats in Jeolla but was hardly the cause.
