Had had two interns in my office. One is a German national, another is a Spanish national. In both cases, they are using visitor visa when entering Taiwan.
Both were spending around 5 months in the company.
You may or may not get paid for the internship. (depends on the company)
Before you arrive in Taiwan, you need to make sure that:
1. you are registered as a student. throughout the internship period
2. your nationality belongs to the "permitted" ones.
(Nationals of Australia, Belgium, Canada, the Czech Republic, France, Germany, Hungary, Ireland, Japan, Korea, New Zealand, Poland, and Slovakia using multiple entry visitor visa valid for 1 year)
(Nationals of UK using single entry resident visa valid for 3 months)
(Nationals of Austrian using multiple entry visitor visa valid for 6 months)
Details see this link