The building beside AIT is national headquarters. People that reside in Taipei go to a different location.
This one for Taipei.
衛福部健康保險署臺北業務組-健保大樓辦公室
100, Taipei City, Zhongzheng District, Gongyuan Road, 15-1號
02 2523 2388
https://goo.gl/maps/UhhTQDau75P2
This site tells everyone in Taiwan where to go in their district for NHI related services.
https://www.nhi.gov.tw/english/Content_List.aspx?n=20A93E4CE83C5762&topn=ED4A30E51A609E49