You need an ETA for Guam if you have a Taiwanese passport

Travellers need a travel authorization to visit Guam for Business or Tourism. The Guam and the Commonwealth of the Northern Mariana Islands Electronic Travel Authorization (GCNMI ETA) is an online application that determines the eligibility of visitors to enter Guam. Once the application is approved, travellers receive their GCNMI ETA confirmation electronically. A valid GCNMI ETA is required to visit the country. If the GCNMI ETA is expired or doesn’t match the traveller’s passport information, travellers will not be able to board their flight. A GCNMI ETA is electronically linked to a passport and valid for 2 years. If travellers receive a new passport, they must apply for a new GCNMI ETA. United States permanent residents or holders of valid United States visas don’t need a GCNMI ETA. Travellers must be residents of Taiwan who begin their travels in Taiwan and who travel on direct flights from Taiwan to Guam or the CNMI without layover or stop, except that the flights may stop in a territory of the United States en route. Travellers must have a Taiwan National Identity Card and a valid Taiwan passport with a valid re-entry permit. Please see the source for more details.