Mt. Nanhua lie within the premises (within the Ecological Protection Areas) of Taroko National Park and so a Park Access Permit, in addition to a Mountain Access Permit, are both required. Mt. Qilai South Peak required a Park Access Permit.
Please note that lodging for this route (Tianchi Cabin) is normally done by a lottery process run by the Nantou Branch, Forestry and Nature Conservation Agency: https://tconline.forest.gov.tw/room/