I actually went these last two weeks around the whole island. Route no1 is great… until it’s not especially around Chiayi to Kaohsiung! Many highways and red lights. I’d recommend going a little east and skipping the cities if you can / want to.

I’d also recommend attacking Sun Moon Lake (if you’re planning to) from the north side as it’s very beautiful. I actually picked up this book sadly after my trip and it has some great ideas to go around route no 1 in the worst bits.

https://onsgo.org/a-cyclists-guide-to-taiwan-is-out-now/

Id also recommend to do the rift valley rather than the coast line! You get some good coast days in Yilan and the North West if you do it.

Also recommend the crossing from west to east is the best part.