My understanding is working online, providing the “provision of labor” (提供勞務) was outlined by the Ministry of Labor in 2018 as requiring a work permit:
https://laws.mol.gov.tw/FLAW/FLAWDOC03.aspx?datatype=etype&N2=1070507378&cnt=1&now=1&lnabndn=1&recordno=1
(The attached PDF)
The Employment Service Act states in Art. 43 that
除本法另有規定外,外國人未經雇主申請許可,不得在中華民國境內工作。
but does not define work. The Council of Labor Affairs (predecessor to the Ministry of Labor) clarified in 2005 in an interpretation letter (勞職外字第0940503946號函 ) that an activity does not require a formal contract or even payment to qualify as work, though it also said volunteer work in accordance with the Volunteer Service Act does not require a work permit.
In 2015, the Ministry of Labor issued another inte…