Originally Posted by
myperks
Taiwanese passports can use eGate for free and can sign up for it upon arrival. Takes like 5 minutes.
As for the compulsatory military service, it doesn't matter which passport you enter with, they are all connected and if you have the overseas Taiwanese permit and not stay overstay certain of days per year, you can enter with a non Taiwanese passport (even if you have one). So if your sons can exit Taiwan, that means they have the oversea Taiwanese (exit) permit AFAIK.
I’m not sure if you are correct about all the passports are connected. I was born in Taiwan and immigrated to the US when I was 14. I waited till I became a US citizen and got a US passport before I went back for the first time. I have gone back 10+ times with my US passport since and never had to deal with any issues exiting. I’m always treated as a US citizen even though I was born a Taiwanese citizen and my first passport was Taiwanese.