Taiwan's idn ccTLDs 台湾 and 台灣 were entered into the Root Name Servers on 14th July 2010. This does not though mean that they are now live. Taiwan's Registry Name Servers have not yet been set up to resolve 台湾 and 台灣.
The current situation is that a lookup of 台灣 gives the result "Non-Existent Domain". A lookup of 台湾 gives more interesting results. The Registry Name Servers are using DNAME to map 台湾 to 台灣 which, currently, is a non-existent domain.
I used www.simpledns.com/lookup-dg.aspx to perform a DNS delegation trace of 台湾 and 台灣 to determine the current state of Taiwan's Registry Name Servers. I used Taiwan's National Central University's web addresses for my tests. Their working addresses are: