Are street numbers in Taiwan addresses in geographic order, like in Australia and the USA, or are they in chronological order, as often happens in Japan?
They're in geographic order. However, long Taiwanese roads are broken up into "sections" (段), each of which restarts the numbering. So if you look at these two addresses:
#456, Xinyi Rd Sec. 4, Xinyi District, Taipei City #16, Xinyi Rd Sec. 5, Xinyi District, Taipei City
"#16" (Sec. 5) is actually further away from the city center than "#456" (Sec. 4).
In practice, though, most street numbers (號) are in relation to alleys (弄) and lanes (巷), not the main road. Put it all together and you get something like this:
12 F, #88, Alley 10, Lane 78, Xinyi Road Sec. 4, Xinyi District, Taipei City 10204
Wikipedia goes into a bit more detail.