It's very difficult to get Incheon airport form Gyangsan. It's not because of transportation but it's because of timing. One of my friends called me from airport today, he went there to receive his wife. Her arrival time is 00:05 at mid night. Certainly, it will take few few minutes to cross the security, custom and immigration etc. My friend arrived at the airport at 5:00 PM. The reason he arrive early is he had no choice. There is only limited direct bus to Incheon airport from his place. Now, he has to wait until 07:20 tomorrow morning to get another bus to go back to his home in Gyangsan. He will spend more than 24 hours on the way.
From Gyangsan, there are only 4 direct buses per day to Incheon airport. It's at 00:30, 03:20, 07:20, and 11:10. He has taken the last bus, 11.10's bus, and arrived at the airport around 16:20 PM. From 16:20 to 07:20 in the morning, total of 15 hours, he has nothing to do in the airport except look around and see the people departing and arriving. If he is families with Korean Chimjilbang, he can enjoy in the basement of Incheon airport. There is a nice Chimjilbang.
There is some another way to get to Incheon airport. It's from Dong-taegu. They have more frequency then the limousine bus from Gyangsan, Sa-taegu and Bu-taegu. The information about the bus schedule is here in this link.
It's far better to take flight from Taegu or Busan, if available.