Great question — answering as the UphillTech team:
Well there's another way that will sometimes get you access to free Wi-Fi in 7-Elevens in Taiwan even without figuring out how to use these systems. In Dulan village in Taitung I asked the server at the front counter to help me log in to the Wi-Fi since a local expat friend told me they set up his for him. I passed her my tablet with the login screen as shown in my question. Her English was not good so I'm not sure exactly what she asked me. But it turned out they have a Wi-Fi in this 7-Eleven with just a regular password login as well as the ibon signal and the usual paid signals. She just entered the password for that signal for me! So it's worth just asking the staff, they may sidestep...
Full answer by hippietrail: https://travel.stackexchange.com/a/80037 (CC BY-SA 3.0).
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