@yyy seems to have the best answer, I recall one response on the subject that said the issue often is that business owners register a cram school as just that, and fail to register the kindergarten as a separate entity. From my understanding it is not explicitly illegal to work at a kindergarten, but rather that there is a right and wrong way to do so. And that’s what makes the gray area you mentioned.
There’s so much information on the subject, it is often hard to decipher which is accurate. @yyy often uses direct citations to Taiwanese law. On the other hand, I’m not a good source for information. I’ve only been in Taiwan for 9 months and mostly quote from personal experiences. That is why I told @Itsmeee to re-read the information they are quoting, seems they misunderstood it.