There are indeed at least two vācaspatimiśra authors. The earlier author wrote nyāyakaṇikā and other philosophical commentaries, as well as one treatise, tattvabinduḥ. The scholarly consensus is that he was active in the 11th century CE. See pages xviii and following in the introduction to tattvasamīkṣā edited by Diwakar Acharya (Vācaspatimiśra’s Tattvasamīkṣā The Earliest Commentary on Maṇḍanamiśra’s Brahmasiddhi, Stuttgart, 2006) for recent dating information on the earlier vācaspatimiśraḥ (Vācaspatimiśraḥ I). Ludo Rocher distinguishes two vācaspatimiśra authors and a third with similar name in the introduction to his edition Vyavahāracintāmaṇi A Digest on Hindu Legal Procedure, Gent, 1956. Karin Preisendanz distinguishes the two vācaspatimiśra authors in the introduction in part 1 of Studien zu Nyāyasūtra III.1 mit dem Nyāyatattvāloka Vācaspati Miśras II (Stuttgart, 1994). I don’t keep up with all of the secondary literature on vācaspatimiśraḥ, even through I am nearing the end of a long running critical edition of vidhivivekaḥ and nyāyakaṇikā, but I find it difficult to accept that any scholar can identify the two as one, any more than we can identify maṇḍanamiṣraḥ, the author of vidhivivekaḥ and other works, with Dr. Mandan Mishra.

Elliot