The Verdict: Need More Info
Taiwan is on the Czech list, but its age limit and quota are not published. Ask the Czech Economic and Cultural Office in Taipei for the current terms and whether places remain.
Visas under the other agreements last up to a year, with work incidental to travel, and set ages of 18 to 30 or 18 to 35. Expect something similar, but confirm it; the usual fee is CZK 2,500.
Taiwan is also one of the thirteen nationalities in the Czech digital nomad programme, which suits IT and marketing workers, lasts longer and counts towards permanent residence. That programme excludes anyone who held a Czech long-term visa in the past year, which a working holiday visa is, so decide the order first.