Crossposted from our email conversation:
I have not heard of any rule that you cannot hold work permits in
different industries. I’m not saying that it isn’t true though. There
are certainly more absurd rules than this one.
The only thing close is the prohibition on white collar professionals
from taking a blue collar job as a new or second job. (Blue collar
workers are not allowed transfers or second employers at all.)
However, there is no restriction in the law limiting a white collar
professional to only one type of white collar job.
The law on second work permits is in Article 53 of the Employment
Services Act and is very clear on the restrictions. There’s nothing
in this article which would prevent a computer programmer from taking
a teaching job, though you could not for example take a construction
worker job. (Not that I expect you’d want to.)
However, I also know very well that it is quite common to get
incorrect information, even from officials who should know better.
Because of this, I would not rely on such advice until all avenues
have been exhausted. It is a fact of life in Taiwan that one has to
be persistent when dealing with officials to get things done.
Therefore, I would suggest you disregard this advice and attempt to
get one anyways. Your second employer would apply for your work
permit as normal, and you need to meet the qualifications of the type
of work permit. If it is granted you need to amend your ARC to add
the second work permit.