The airport is connected by light rail, not directly by Busan Metro
Gimhae Airport has its own Airport Station on the Busan-Gimhae Light Rail Transit. The light rail connects with Busan Metro Line 2 at Sasang and Line 3 at Daejeo. If you are heading to central Busan, your actual journey may therefore include a light-rail ride plus a metro transfer.
Late arrival: check the last usable connection, not just the last train
A final light-rail departure is only useful if the transfer line you need is still running when you reach Sasang or Daejeo. Before a late flight, route your full trip to the hotel using current operator information and check the final usable connection. Bus schedules also vary by route and can change, so do not rely on an old airport blog or screenshot.
Know the taxi fallback before you need it
Korea Airports Corporation currently lists the standard Busan taxi base fare at KRW 4,800 for 2 km. It also lists nighttime surcharges of 20% from 23:00 to midnight, 30% from midnight to 02:00, and 20% from 02:00 to 04:00 for standard taxis. The airport page gives example estimates such as KRW 18,000 to Seomyeon, KRW 20,000 to Nampo-dong and KRW 25,000 to Haeundae or Gwangalli, but traffic and destination details can change the actual meter fare.
Domestic and international terminals are separate
If you need to move around the airport complex, KAC currently lists a free airport shuttle running roughly from 05:00 until 22:48 at 12-minute intervals, serving the international and domestic terminals and parking/cargo areas. Do not treat that internal shuttle as a city transport service.
Best practice for a late flight
Before takeoff, save your hotel's Korean address and compare: full light-rail-plus-metro route, any current airport bus, and a taxi estimate. If the public-transport margin is small, plan the taxi fallback in advance rather than trying to solve it after the final connection has departed.