It depends on what jobs you are looking for. As far as I know, many private language teaching units in Taipei are willing to hire native speakers who also speak Mandarin. However, many of these units won’t help you get working visa due to the bureaucratic official procedure. It means that you are actually working illegally if you work for one of those units.
Your mother tongue is the advantage. I knew some transnational companies in Taipei and even some local business consulting companies, international trade agents, and travel agents that are willing to hire expats. Once again, however, the policies concerned with foreign nationals’ employment in Taiwan are not well-suited to respond to demands of both local employers and potential employees.