Yes EVA will help you book a room at their preferred transfer hotel if you have a long layover.

I just came back from a DPS-TPE-YYZ last Saturday and the TPE-YYZ had a 22 hour layover. After I got off the plane from DPS they had agents direct all transfer passengers to the transfer desk and when you approach the desk you should see a few agents, one of whom should have your name on a board. They'll collect you at the transfer desk, confirm that you have the necessary visa's to enter Taiwan, and then hand you a voucher for hotel and breakfast the next morning. I was sent to the Monarch Plaza in Taoyuan city about 15 mins drive from the airport. I inquired if I could choose a different hotel closer to Taipei but was told that they are currently only booking complimentary hotel stays at the Monarch Plaza.

I was on a paid J ticket though so don't know if STPC is influenced by class of travel. I did see some Y passengers being directed to the transfer desk as well but don't know if they were given STPC.