Hakim Ali Gilani died on 14 Dhu al-Hijjah 1017AH, or 22 March 1609.
Sources
For evidence regarding his life, see:
Carl Brockelmann, Geschichte der arabischen Litteratur, Supplement, 3 vols. (Leiden: Brill, 1937-1942). , vol. 2, p. 626.
A. Z. Iskandar, A Catalogue of Arabic Manuscripts on Medicine and Science in the Wellcome Historical Medical Library (London: The Wellcome Historical Medical Library, 1967), p. 182.