Taiwan provides free public Wi-Fi with 8Mbps bandwidth in government-run indoor public areas with the SSID (Service Set Identifier) iTaiwan. The main site to learn about this service is 首頁 | iTaiwan無線上網服務.
You need to be near a government office or near some government-run area during operation hours to find the network. For example, the township building probably only runs 9-5 but the train station should run 24 hours a day. It is meant to be indoors, so signal is often weak when outdoors. (And it could be a bad actor trying to imitate iTaiwan to steal your data.)
I rarely use it, but I vaguely remember that, the last time I used it, it seemed to reset every 15 minutes or so, meaning that I had to go back through the agreement page.
Given the limitations of location and speed, I find that a data SIM or enjoying free Wi-Fi with tea or lunch often works better.