After seven long years, the SBL finally had an official website of its own that contains real-time score and box scores. Up next, I think the league will have an English website… in 10 years.
Anyway, the SBL website is hosted under the CTBA (Chinese Taipei Basketball Association) which operates the SBL. The URL is http://sbl.basketball-tpe.org/
For those who understand Chinese, feel free to check the box scores on the website. It also contains a section of game results and box scores in the past seven years but the section appears to be under construction at this moment.
The league's partner Chunghwa Telecom -- Taiwan's largest landline, mobile phone and internet operator -- also presents a SBL website at http://sports.hinet.net/sbl
The Hinet website does not provide box scores, but it does provide live streaming and videos on-demand.