Unofficial translation:
1. According to the provisions of Art. 43 of the Employment Service Act (hereinafter the Act): “Except as otherwise provided for in thist Act, a foreigner for whom a work permit has not been applied for by the employer shall not work within the borders of the ROC.”, and furthermore, the Council of Labor Affairs (now changed to the Ministry of Labor) in 2006-02-03 Lao Zhi Wai Zi letter #0950502128 states in part that what Art. 43 of the Act calls “work” is definitely not determined by the outward form of the contract or whether or not there is remuneration, but if in fact the foreigner is providing labor or work, even if there is no compensation, it is still categorized as work.
2. Based on what is written in Sir/Madam’s message, for a foreigner residing (or staying) in Taiwan visa-free or with a visa, providing labor in Taiwan via the Internet to an individual or company outside the borders of the ROC in exchange for remuneration, if the natural person or juridical person [company etc.] receiving Sir/Madam’s labor is within the borders of our country, then it is necessary in accordance with the Act and the relevant provisions to apply for a work permit, and after the approval by this Ministry [of Labor], [Sir/Madam] can work in Taiwan. If the natural person or juridical person engages in work within the borders of our country without approval by this Ministry, it shall be handled as a violation of the provisions of Art. 43 of the Act, and one may be ordered to leave the borders [i.e. be deported].
That seems to mean that if the only aspect of the work is your physical presence in Taiwan, whereas the website/person/company you work for is overseas and is not receiving your work through any kind of local representative office etc., then you don’t need a work permit. 
I don’t doubt Tando, but I still would take a “scientific” approach: can this statement from the MOL be replicated? 