Whenever the Prophet got up for Tahajjud prayer he used to clean his mouth (and teeth) with Siwak.
It’s a bit weird for me because if I wake up for Tahajjud, I don’t want to make any extra effort. Doing miswaak at that time seems a bit too much. But that’s MY problem, and I need to fix it. If Prophet (SAW) did it, I should too.
Plus, there’s a nice effect of miswaak on your prayer. Makes you fresh and ready for `ibaadah. (y)