Your trip falls in
peak typhoon season for Taiwan (July–October). This doesn't mean one will hit, but be prepared:
Before traveling: Monitor
CWA (Central Weather Administration) and the
Joint Typhoon Warning Center
If a typhoon is declared: The government announces "typhoon days" — offices, schools, and many businesses close. MRT may stop. Stay indoors.
What to pack: Compact rain jacket, sturdy umbrella, waterproof phone case, dry bag for electronics
Average rainfall: Taipei gets ~320mm in August, ~240mm in September. Brief heavy downpours are common even without typhoons.