The article I shared said that Zih Ciang Dorm 10 has singles and doubles. It mentioned that 3rd and 4th year undergrads are lucky to draw singles. The most authoritative source of information about this accessible to you is likely to be the Office of International Affairs.
If you are looking off campus, you might also see if you can find something in the Wanfang Community area two MRT stops away. Another possibility is this area behind the campus but not up the hill.
My personal experience has always been that it is best academically to live as close as possible to the school.
If you are looking in a specific area, the easiest approach in Taipei for a newcomer is to go to a local realtor in or near the target area. There will usually be several. Most but not all handle rentals as sideline. They will know of more and better places than you can find online. They usually charge one month of rent as a finder fee. Typically, you will need to put up two months of rent with the landlord as a security deposit.
I worked in policy at the ICDF back in the day (in my very early 20s), and the education and training programs were run by the education and training department at the ICDF with the generous scholarships being given to allied countries. In the KMT years, Taiwan often paid for scholarships for allied country selected citizens to go to Yale, Harvard, etc. However, in the first DPP term under Chen, it was “Taiwanized” so that allied country recipients still got free and full scholarships, but they had to come to Taiwan for Taiwan studies, MBA, agriculture etc. type of degrees, including at NCCU. So, if you are from an allied country, I think it’s pretty generous and not that competitive in terms of applicant numbers. Keep in mind, I haven’t worked there in 20 years!