I don't feel qualified to interpret the document excerpts quoted below; I'm merely posting them in case anyone can get any use out of them. Nothing in this post is meant to gainsay in any way what sewersquid wrote, or what anyone wrote, for that matter. I don't know anything firsthand about the actual, practical particulars of getting a job as a student here. I'm just posting some stuff that I found on the Internet.
This appears to be an English translation of a regulation pertaining to the granting of student work permits, from a document on the Ministry of Labor website, entitled "Regulations on the Permission and Administration of the Employment of Foreign Workers":
Article 31 Should a Foreign Student as referred to in Article 30 have been officially enrolled in a school to take courses for 1 (1) semesters or more in a division, department, or graduate institute thereof, or to take language course(s) for one (1) year or more, and have had an outstanding performance in academic accomplishments, and should the school in which he/she is enrolled have acknowledged the existence of any of the following factual situations, the said Foreign Student may engage in jobs relevant to the course(s) he/she takes and language he/she learns:
1. It is proved by concrete evidence that the financial situation of the said Foreign Student is unable to continuously sustain his/her studies and living.
2. The teaching or researching unit of the school in which the said Foreign Worker is enrolled is in need of his/her assistance and participation in teaching or researching work.
3. The said Foreign Student has to engage in off-campus practical training related to the course(s) he/she takes.
Foreign students who meet one of the following qualifications are not restricted by the provisions as referred to in the previous Paragraph:
1. Foreign Students with exceptional specialty in a foreign language, with the ad hoc approval by the Ministry of Education, after his/her enrollment in the school, to work on a part-time basis as a teacher in that language in a subsidiary language center affiliated with a University/College or with a foreign culture and education organization stationed in the Republic of China.
2. Foreign Students enroll in a graduate institute and have been approved by the school in which the said Foreign Workers enroll to conduct relevant researching work.
This appears to be the original Chinese version of the translated excerpt above, bearing the Chinese title "雇主聘僱外國人許可及管理辦法," and taken from the Ministry of Labor website: