Note:
(a) I can not find out when Taiwan exempted Singaporeans visa requirement, and vice versa.
(b) Shih Hsiu-chuan, Malaysia Grants Visa-Free Privileges. Taipei Times, Mar 19, 2011 www.taipeitimes.com/News/taiwan/archives/2011/03/19/2003498580
("Taiwan has offered visa-free travel to Malaysian citizens since 2002")
(c) Further, Taiwan exempts visa for passport holders of Thailand and Brunei from Aug 1, 2016 to July 31, 2017.