The new Danhai Light Rail system is now operational. Currently the trains run about every 20 minutes which is great if you’re site seeing, but for commuting it’s less than ideal.
If you’re headed to Tamgang University 淡江大學 it’s pretty convenient and will only set you back NT$20. The fee for stops 1 thru 7 from Hongshulin is NT$20 for one trip. The fee fee for the remaining stops assuming you are coming from Hongshulin is NT$25 for each trip.
If you’re transferring from the main Taipei MRT Red line there’s a discount for the LRT trip, of up to around 20% discount for the LRT trip.
The Danhai LRT starts at Hongshulin (紅樹林) and ends currently at Kanding (崁頂)。
For train times and fee details see this write-up: https://zh.m.wikipedia.org/wiki/淡海輕軌, also here’s a list of the current times: