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

Travelers need a travel authorization to visit Guam for Business or Tourism. The Electronic System for Travel Authorization (ESTA) is an online application that determines the eligibility of visitors to enter Guam. Once the application is approved, travelers receive their ESTA confirmation electronically. A valid ESTA is required to visit the country. If the ESTA is expired or doesn’t match the traveler’s passport information, travelers will not be able to board their flight. An ESTA is electronically linked to a passport and valid for 2 years. If travelers receive a new passport, they must apply for a new ESTA. United States permanent residents or holders of valid United States visas don’t need an ESTA. Travelers 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. Travelers 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.