I looked at the results for Case 14 and as expected theres zero precints that voted Yes.
http://referendum.2018.nat.gov.twTaipei City - 38%
New Taipei City - 34.9%
Hsinchu City - 34.2%
Keelung City - 33.9%
Yilan County - 33.1%
Tainan City - 33%
Kaohsiung City - 32.5%
Chiayi City - 32.1%
Taoyuan City - 31.8%
Taichung City - 31.2%
Pingtung County - 30.6%
Hsinchu county -30.4%
Yunlin county - 29.7%
Chiayi County - 29.6%
Changhua County - 29%
Penghu county - 28.9%
Miaoli county - 28%
Nantou County - 27%
Hualien County - 26.4%
Taitung County - 25.8%
Lienchang county - 25.4%
Kinmen County - 24.3%
Within Taipei.
Neihu District - 39.1%
Datong District - 38.9%
Zhongshan District - 38.6%
Shilin District - 38.1%
Da’an District - 37.8%
Beitou District - 37.7%
Songshan District - 37.5%
Nangang District - 37.5%
Wanhua District - 37.2%
Xinyi District - 36.7%
Zhongzheng District - 36.1%
Wenshan District - 36.1%
https://web.cw.com.tw/election2018/electorate/index.html?county=63000Using this map the reason for Neihu being higher(despite it still being pretty low...) is the higher number of young voters there.
Only three districts in Taipei were the vote against marriage being one male and one female reached 40%.
Dahuli, Neihu 40.9% (In the referendum to allow same sex marriage it was 43.2%, god bless those inconsistent 2.3% of voters)
Zhongyuanli, Zhongshan District 41.3%
Tianshouli, Shilin District 40.1%
Then in the vote to allow same sex marriage there were a few ironic districts that voted Yes to Marriage being one man and one woman AND at the same time to allow same sex marriage
Bojiali, Wenshan 65.3% to first / 45.3%
Considering Bojiali also has a higher number of elderly voters it could just be a lot of elderly voters either voted Yes to everything because they didnt like referendums OR didnt read clearly the one to allow same sex marriage.