The Prophet ﷺ remained standing until it grew very light, then he set off before sunrise, taking Fadl bin Abbas as his companion behind him on the mount... the rest of the hadith.
فلم يزل (يعني النبي ﷺ) واقفا حتى أسفر جدا، فدفع قبل أن تطلع الشمس، وأردف الفضل بن عباس… الحديث.
Muslim narrated it in the Hajj chapter (1218) via Hatim bin Ismail Madani, from Jafar bin Muhammad, from his father, from Jabir, and he related the hadith in full.It is part of the sunnah that the pilgrim should depart from Muzdalifa before sunrise. Tawus said, "The people of pre-Islamic ignorance used to depart from Arafah before the sun set, and from Muzdalifa after the sun had risen, so Allah delayed this one and made this one earlier."