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I'd wonder who is the king of the South, except perhaps Egypt, which at this time is unlikely.
Interesting, I've always heard it would happen just before the GT or at it's beginning due to the massive cleanup in Ezek 39.
I would say the end-time king of the South may represent the leader of a confederacy of Arab nations or a powerful Arab nation. As it was historically, Egypt will likely be involved (Daniel 11:42).
Just so we are on the same page.......What is "GT" you mentioned?