Ah, this is interesting. The Canadian TECO’s website says nothing about internship visas* and lists interning as a valid WHV activity, but the Aussie TECO’s website tells a different story, and it turns out the information on BOCA’s website is closer to the Aussie TECO’s info.
*i.e. visitor visas with “FT”, in two flavors: 實習 and 代訓/受訓
https://www.boca.gov.tw/content.asp?mp=2&CuItem=2067 (English)
https://www.boca.gov.tw/content?CuItem=1259&mp=1 (Chinese)
https://www.boca.gov.tw/content?CuItem=1877&mp=1 (受訓)
https://www.boca.gov.tw/content?CuItem=2065&mp=1 (實習)
As for the extension, I would ask the NIA.
http://www.immigration.gov.tw
If it’s difficult/impossible to get an extension, they should let you enter without activating the visa (i.e. get a visa exemption), so you can fly out and in again when you’re ready to start. This would cost you a pair of plane tickets, of course.