How about Yingge Ceramic Area (or whatever it’s called)? You need to take the train about an hour (I believe only the slow ones stop there) and get off at Yingge Station. Lots of stores that sell interesting knick-knacks, in addition to the pottery on sale. My bro in law has a pottery gallery/store there. Here’s a little gift he gave me. He makes better things. This was something made just for fun and not something on sale in his store.
Best bet is to see if the seller of the t shirts has a store front. You can always message them on whatever website you’re using and ask. If they don’t have a site, you can ask to meet them in person to see or try on the shirts.
Don’t let the big names discourage you. Taiwan is very practicle sometimes when naming things and doesn’t really understand the marketing aspect of giving someplace an simple recognizable enticing name. Both places great for shopping.
This 4 level place has gifts of all types and price points from all over Taiwan. Pricing is regulated so no gouging. Taiwan Handicraft Promotion Center, No. 1, Xuzhou Road https://goo.gl/maps/Qh5TYimH4iA2
I love this place. Unique and high quality Taiwan gifts in a beautiful historic building. National Taiwan Craft Research and Development Institute Taipei Branch, No. 41, Nanhai Road https://goo.gl/maps/JWaYDnJ5PU32