Answered by ZUPAN
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Jan. 11, 2020 04:21
Your itinerary would be eligible for 144 hour visa free transit twice, but the problem is with the first part of your itinerary:
Incheon - Xiamen - Kinmen
Although arriving by air and departing by ship is eligible, the problem is how to obtain a ticket for a ship between Xiamen and Kinmen ahead of your travel! It used to be possible through one website that is down now for roughly 8 months or even more. In reality, you need this ticket or at least some kind of an e-confirmation for this Xiamen to Kinmen route before your departure from Incehon because without it, they cannot allow you to board the plane.
Your return journey:
Kinmen - Xiamen - Incheon can be done without any problem because you will book your ship ticket for Kinmen - Xiamen route on the spot and you will also have a flight ticket Xiamen - Incheon in your hand at the moment of your check-in for a ship in Kinmen.
You can try to contact Klook agency and ask them if the can procure you a ticket or an e-confirmation for Xiamen - Kinmen ship ticket, so that you have a proof of your transit intention at your check-in in Incheon.
If this fails, you will have to find an alternative option like:
Incheon - Taipei - Kinmen by plane
and after that to your original route
Kinmen - Xiamen - Incheon
At the time being I really cannot see and other feasible option beside the mentioned one, especially if Klook has no ability to make a reservation for a ticket from Xiamen to Kinmen.