You can also link Korea to Latin America through immigration. Koreans have immigrated to many Latin American countries, especially Argentina. The numbers are small (~22,000 in Argentina, according the Ministry of Foreign Affairs of South Korea).
Another interesting way to connect Korea to Latin America might be through food. Korean-Mexican fusion food has grown in popularity, especially with the Kogi truck and Roy Choi. Also, at least here in Los Angeles, most of the people who are actually cooking the food in Korean restaurants are Latin immigrants.