The link to the NHI offices is broken (404):
https://taiwangoldcard.com/goldcard-holders-faq/health-insurance/
But it seems even the link from nhi.gov.tw is also broken, so I'm not sure we can do anything about it at the moment:
https://www.nhi.gov.tw/English/Content_List.aspx?n=20A93E4CE83C5762&topn=ED4A30E51A609E49