I would like to visit Taipei at the end of July on a tour by railway.

Generally, there will be frequently & lightly rainy days during that time; however, still several cloudy days. Therefore, you can pay attention to the weather report in advance! Then may be you will lucky to view the nice scenery from the train!

Though, it will be during the typhoon season, so there is still likeliness that your trip may be spoiled. If you don't mind, I would suggest you change your plan to Oct. or Nov.