When I first started my international school job search I focused on South Korea because I had taught EFL previously. What I found was that a lot of international schools in Korea don't pay very well and the really good ones tend to hire at fairs. Frankly, I've had way better offers in China. If I were you I would apply to jobs in other countries. As for EFL jobs in Korea, I wouldn't go down that route. Employers are hit and miss and the benefits aren't as good as what you would receive from an international school. Plus, if you do take an EFL position, it doesn't count as proper teaching experience. I've read that some teachers have had difficulty getting an international school job if they taught EFL too long.