There are a few bands which do Taiwanese songs almost exclusively. One of them is 滅火器/Fire EX. They tend to go for a more rocky style than most other Chinese-language musicians that I’ve come across. Here are three of my favourites:
I can understand maybe 50% of each – there’s a higher frequency of basic vocabulary than found in Mando-/Cantopop songs, for whatever reason.
Funny story: I heard the last song (欲走無路) multiple times before realising it wasn’t Mandarin, which shows how much attention I was paying, and how lousy my Mandarin was at the time. I was very disappointed to find that these cool rock songs weren’t Guoyu!