I need to get to Taitung (from Taipei) on the moon festival weekend. I planned this in July, but I was told that I could not buy train tickets until 2 weeks before the trip. Well, I was going to buy them on friday morning (2 weeks before the trip), but guess what, they’re sold out already. Is there anyway to get down there. I know this is a holiday weekend so its a longshot. Maybe somebody can give me some advice?
HSR to Kaohsiung, then southern link rail to Taidong maybe?
Every train is sold out including trains going both directions around Taiwan?
edit - internet ticketing closes at midnight but you can check here to possibly find a ticket railway.gov.tw/en/CP.aspx?sn=3537&n=6792
You can’t buy train tickets until two weeks b4 and if you want one you have to be up before 6AM with your finger on the mouse button when the sales open at 6:00 on the dot. Then the server fails due to demand load and the travel agents and employees of Taiwan Rail scoop all the tickets up to sell to friends.
The only way to go is to fly. Less than 2000NT and only 50 minutes.
Here is a sample procedure for an assumed trip down the east coast that is based on how i usually get the tickets i need: first you buy a set of tickets at the railway station, without seat reservations if those are not available: for example, one from Taipei to Loutung, one from Loutung to Hualien, one from Hualien to Ruisui, and one from Ruisui to Taitung. If any of those tickets come without seat reservation, go back to the railway station starting two days before your trip and request an exchange for tickets with seats if possible. Repeat those trips to the station from time to time until all your tickets have been exchanged that way (last try would be half an hour before the train leaves). Finally, if you end up without a seat reservation for any of those segments, look for an empty seat while underway and sit there until someone claims the seat (repeat this procedure as necessary). You may end up standing for part of the trip (until now i never have, and neither have any of the other people for whom i’ve made reservations). (Since i have not taken that route, i don’t know how well this approach would work for the west coast and southern link railways.) Anyway, if this procedure is too cumbersome, try traveling on different days (not Friday and not Sunday) or take the plane. 
