Fill in the e-Arrival Card online before you fly and you skip the paper form and the queue for a pen — same details, done sitting down. Then immigration, bags, and buy and top up a T-money card at the CU or GS25 in the arrivals hall before you leave the airport — it works on the AREX, and on every Busan metro and bus for the rest of the trip. Give yourself a full hour from touchdown to being on a train; mid-afternoon is one of ICN's busiest arrival windows. With the train not leaving until 21:28, that hour costs you nothing.
Smart Entry Service (SES) — skip the immigration queue, if you qualify
SES is Korea's automated immigration gate: passport on the reader, scan the finger the screen asks for, look at the camera, walk through. No officer, no queue — and once you're enrolled it's permanent, so it pays off across trips rather than just this one.
Who can enrol: foreign nationals aged 17 or over who hold either a Hong Kong, Macao or US passport (countries with an MOU), a Korea Priority Card, or an Alien Registration Card / Domestic Residence Report if you live in Korea. Under-17s and passports outside that list can't — most short-stay visitors, Taiwan included, still queue at the counter.
How: in person at an enrolment centre, taking your passport; they capture your fingerprints on the spot and it takes minutes. There are centres at Incheon and Gimpo, at Busan, Jeju, Daegu, Daejeon, Gwangju, Suwon, Cheongju and Seoul immigration offices, and at Seoul Station and the City Airport Terminal. Note it isn't a desk you pass on the way through arrivals — if you're enrolling at Incheon, look up the centre's location and hours first and allow time for the detour.
Where it then works: the SES gates at Incheon, Gimpo, Gimhae (Busan), Jeju, Daegu and Cheongju airports, and the Busan and Incheon ports. Gimhae matters if you ever fly into Busan directly instead of taking the KTX.