Covered here:
http://netbuz.org/blog/2011/11/x-bells-and-urgency-hints/
I'm going to try this.
Update: Works like a charm. As a note to future-me:
1. Remember to re-source your .tmux.conf, or quit all tmux sessions.
2. While pre-occupied with remember #1, remember to re-merge settings in ~/.Xdefaults.
