For a serious or potentially life-threatening emergency in Korea, call 119. The National Fire Agency's emergency guidance says callers should explain that there is a patient, give the location, and describe what happened, including consciousness and breathing. If you do not know the exact address, give a nearby major building or other location marker and keep your phone's GPS on.
For a non-life-threatening problem at night, on a weekend or during a public holiday, use the government's Emergency Medical Portal E-Gen to look for medical institutions and pharmacies that are open. Ministry of Health and Welfare guidance also points people to 129, 119 and local 120 call centers for information on open clinics and pharmacies during holiday periods.
Do not assume a directory listing guarantees that a clinic can treat your exact problem or that a pharmacy can fill a particular prescription. Hours, departments and registration cutoffs can change, especially on holidays. Call the facility before traveling when possible.
If symptoms seem severe, do not spend time comparison-shopping clinics. Call 119 and follow the dispatcher's instructions. For milder problems, use E-Gen to identify a nearby open clinic or pharmacy and confirm by phone before going.
Practical next step: save 119 in your phone, bookmark E-Gen, and keep the Korean name/address of your accommodation available so you can describe your location quickly.