At any point in time post Japanese occupation and Korean War, and before Park Geun Hye's presidency, set up the conditions needed for a South Korean civil war and its consequences.
If you're talking about fighting between rival factions in the ROK Army, that's certainly possible, but I think South Korean society is too heavily integrated, socially speaking, to create a political, protracted civil war (you sound like you're talking about something the Spanish Civil War and not the long train of actual ROK coups). Any actual war between army factions would probably see a substantial US intervention to get the situation under control before the Norks come knocking. Limiting the time period to before Park's presidency means we can't talk about whatever is going on right now, but that's probably for the best.