I knew how this worked in FreeBSD, and fortunately it works in the Red Hat world as well. First, make a backup of your existing timezone file, the create a symbolic link to your timezone. I've seen people copying the file instead, but I feel safer linking.

# mv /etc/localtime /etc/localtime.back# ln -s /usr/share/zoneinfo/Singapore /etc/localtime

I'm tempted to set my timezone to Reykjavík, it's HOT in Sydney today. Nagato Yuki has the right idea. A-heh-hem.

UPDATE: @dai1311 on Twitter says that this also works on Arch Linux. Incidentally, his avatar is of Yuki!