I'd honestly try to split that time up between Taiwan and another nearby destination that you haven't been to (or just want to return to). We love Taiwan, but 12 days would be bordering on the higher end of time that we'd like to spend there. Spouse is from Taiwan and so has family and friends there still that we interact with and hang out while there, but simply from a tourist perspective, I have not enjoyed our longer trips to Taiwan. Ok, maybe writing that I haven't enjoyed our longer trips to Taiwan is a bit of an exaggeration, but by then I'm ready to move on, even if I enjoy being in Taiwan overall. A nice medium for us earlier this year was splitting our Asia trip between Taiwan and Thailand. Next year we plan to split between Taiwan and Vietnam.

If you end up spending the entire days in Taiwan, I'd highly encourage you to travel throughout the island. Take the high speed rail to different areas and enjoy more of what Taiwan has to offer outside of Taipei. One city I haven't been to but where we will visit next time is Tainan as I've recently learned that it is considered the culinary capital of Taiwan

Just my subjective opinion. Others will disagree.