Whenever the Prophet (ﷺ) got up for Tahajjud prayer he used to clean his mouth (and teeth) with Siwak.
Sahih al-Bukhari Book 19, Hadith 17
← Previous Hadith `Abdullah said, "One night I offered the Tahajjud prayer with the Prophet (ﷺ) and he kept on standing till an ill-thought came to me." We said, "What was the ill-thought?" He said, "It was to sit down and leave the Prophet (standing)."

Sahih al-Bukhari Book 19, Hadith 16 Next Hadith → A man said, "O Allah's Messenger (ﷺ)! How is the prayer of the night?" He said, "Two rak`at followed by two rak`at and so on, and when you apprehend the approaching dawn, offer one rak`a as witr."

Sahih al-Bukhari Book 19, Hadith 18