Hi Dancerox,
It's been too many years since we visited Taiwan so I have no specific shop or night market suggestions for you. I can't think of much from Taiwan that I would describe as "unique findings and charms". Many Taiwanese manufacturers now operate factories in mainland China. There is still a strong hematite (mostly man made hematine) industry there producing clasps and beads.
There are some beads and ornaments that are native or aboriginal Taiwanese from tribal groups that were there before the Nationalist Chinese took refuge in Taiwan from the Communists. We found those at touristy places and some historical sites and museums. I don't know if they were made for the tourist trade and/or actually made by the tribal people.
Hopefully others will jump in here with more recent information for you,
Are you also looking for beads?