You indeed bought a Japanese set which only has 4 flowers.

You wouldn't need a specific Taiwanese set but simply a standard Chinese set to play TW rules.

Like this Asian Home Traditional Chinese Version Mahjong Game Set https://www.amazon.com/dp/B001NW0B4E/ref=cm_sw_r_apan_i_MAHNY2CHEA6F17XVRYGE?_encoding=UTF8&psc=1