I never saw the Messenger of Allah ﷺ recite any portion of the night prayer while sitting until he grew old. Then he would sit during it and recite, and when forty or thirty verses remained, he would stand and recite them, then prostrate.
حدثنا أحمد بن عبد الله بن يونس حدثنا زهير حدثنا هشام بن عروة عن عروة
ما رأيت رسول الله ﷺ يقرأ في شيء من صلاة الليل جالسا قط حتى دخل في السن فكان يجلس فيها فيقرأ حتى إذا بقي أربعون أو ثلاثون آية قام فقرأها ثم سجد
Muslim reported it in the Book of the Prayer of the Traveler, chapter "The permissibility of the supererogatory prayer while standing or sitting, etc.", hadith 731, from the narration of Zuhayr. Bukhari reported it in the Book of Shortening the Prayer, chapter "If he prayed sitting, then recovered or found some strength, he completes what remains", hadith 1118, from the narration of Hisham bin Urwa, through the same chain.