I asked 'Aishah: When would the Messenger of Allah ﷺ observe the witr prayer ? She replied: Any time he observed the witr, sometimes in the early hours of the night, sometimes at midnight and sometimes towards the end of it. But he used to observe the witr just before the dawn when he died.
قُلْتُ لِعَائِشَةَ مَتَى كَانَ يُوتِرُ رَسُولُ اللَّهِ ﷺ قَالَتْ كُلَّ ذَلِكَ قَدْ فَعَلَ أَوْتَرَ أَوَّلَ اللَّيْلِ وَوَسَطَهُ وَآخِرَهُ وَلَكِنِ انْتَهَى وِتْرُهُ حِينَ مَاتَ إِلَى السَّحَرِ