If that’s what you understood, you didn’t read the website I linked to or any of the information I posted. You CANNOT use the visa-exempt entry OR the landing visa to get an ARC.
You MUST get a visa from the visa office. You need an onward ticket from Taiwan to get it. You will be hard-pressed to complete the process in a single day and you should bank on staying in Hong Kong or Macau overnight.
(To add to the discussion of your original questions, in all fairness you posted in the teaching forum, not the visa forum. I’m sorry no-one answered your question immediately after posting in the right forum.)
which, on first reading, I thought was saying you can get an ARC on an exempt entry, but now that I look at it again, it actually just says you can apply for a visitor visa in case you do find a job. Does that mean you can apply for the visa within Taiwan, or what? Seems a little confusing to me.