score:6
Typhoons are the Pacific equivalent of hurricanes, great big storms that only hit occasionally, almost always in the August-October typhoon season, and Taiwan gets an average of 3-4 per year. If a typhoon hits squarely where you happen to be staying, you can expect to be washed out for a couple of days, possibly even briefly stranded if you're out in the countryside if there are landslides that take out roads and railways.
However, between the typhoons (which is 95% of the time), you'll be absolutely fine, with clear fall skies and the occasional random sprinkle. Here's a rainfall chart:
As you can see, outside the sparsely populated east coast (=Hualien), it rains a lot more in the summer than it does in either of Sep or Oct.
Upvote:4
In all probability you'll be fine. Unless you are getting a direct hit from the eye of the typhoon, you'll only experience a day or two of heavy rain and some wind. If your in a big city and shopping/dinning, you wont notice much. If you do find yourself on course for a hit, Taiwan is big enough that you could move to another city and keep out of the way. Just keep an eye on the weather forecasts.