if you are employed and go to work everyday, you should be enrolled through the employeepr regardless of your working hours. If you don’t go to work everyday, if you work more than 12 hours a week, you should be enrolled through the employment.
Almost all of your income should be included to calculate your NHI premium, and the adjustment should be made through the employer, if you are enrolled via the employment.
In Chinese
部分工時員工參加全民健康保險資格之認定原則
https://mohwlaw.mohw.gov.tw/FINT/FINTQRY04.aspx?starDate=00000000&endDate=99991231&no=&n1=&n2=&kt=&kw=84031133&kw2=&kw3=&kw4=&valid=&type=etype_&RowNo=2
There are different rules for some occupations, such as univ. teachers.
Regulations Governing the Deduction and Payment of the Supplementary Insurance Premium of the National Health Insurance
https://eservice.nhi.gov.tw/2nd/