Norquest attended the University of Arizona's Joint PhD program in Anthropology and Linguistics,[2] where he studied under Jane H. Hill and Diana B. Archangeli.
As part of his doctoral research, he participated in a Fulbright fellowship in Hainan, China from 2003 to 2004, where he collected field data on various Hlai languages such as Nadou.
[3] In 2007, he completed his doctoral dissertation on the reconstruction of Proto-Hlai.
[4] After obtaining his Ph.D. in 2007, Norquest was employed as a postdoctoral researcher under J. Stephen Lansing at the University of Arizona, where he worked on quantitative comparative-historical linguistic reconstruction methods[5] and on the Austronesian languages of Nusa Tenggara.
[6] From 2015 to 2016, Norquest was the principal investigator of Reconstructing Language Change and Variation, a National Science Foundation project that aims to provide a revised reconstruction of Proto-Kam–Sui.