Here are more links to sites in Taiwan (not only Taipei) to buy watches. I have not visited some of these places as they are not in Taipei. Some are selling pre-loved and some are selling new. For those selling new watches, I don't think that they are selling on-line but more to promote and educate.
Well here goes:
This site sells new watches:
So does this one.
Pre-loved watches. I believe this shop is not in Taipei.
As is this one.
This is in Taipei.
The usual mantra applies, buy the seller not the product and known what you want to buy.