My answer may be biased, because I spend more time in California than in Korea. However, I believe there is not a lot of employers who are looking to hire a Spanish teacher. This is mainly because Koreans' main focus is to teach English as a second language and Chinese/Japanese as a third language (at school, students can choose which language they want to learn). I am sure some people are very interested in learning Spanish, but I have not seen a single tutoring institution (called Hagwon 학원) that is dedicated to Spanish. If you are looking to get paid while you teach, it may be a challenging path you are taking. Though if you speak fluent English, you probably have a higher chance of getting a job.
Again, my opinion may be biased. Good luck! I hope you find what you want :)