I am hoping to go to Seoul, Korea in the summer of 2013. And I am also hoping to get there on Korean Air Flight 86, which leaves JFK at 12:50 AM (I live in New Jersey, USA) and then arrives Incheon International Airport at 3:50 AM. First, how long is the immigration/passport line at Incheon at 4 in the morning? And to those of you who have arrived in Incheon Airport at 4 in the morning whereas the final destination is in Seoul (or the nearby surrounding area, such as Ilsan or Uijeongbu or Bucheon), whether it is a relative's house, academic institution or a business meeting, how did you get to your final destination from the airport, if you didn't take a taxi? My mom is a bit worried that there would be nobody to pick me up at that hour (although my grandfather is likely able to), and the first train out of the airport leaves at 5:20 AM.
I know that I have asked a few Koreans in my area who has taken flight 86, who said that they had a ride or that they waited for the train, but I feel like it is appropriate to ask here as well.