There is an overview including a mention that the data can be made available, at: https://www.vtnews.vt.edu/articles/2005/06/2005-834.html
In addition, there has more recently been a much larger study involving 3000 vehicles over a couple of years, the Strategic Highway Research Program (SHRP2) Naturalistic Driving Study. Some preliminary data and summaries are freely available, and the study has a mechanism for making data requests. Data are available for a few depending upon the size of the data set and the amount of work needed to extract it. I recently received a data set on driving behavior along lighted and unlighted roads at night with about 1900 "events" and the cost was approximately $3000US to receive the extracted data set. You have to register to get most of the useful information, but you can find out more at: https://insight.shrp2nds.us/
According to the National Highway Traffic Safety Administration website (https://one.nhtsa.gov/Research/Human-Factors/Naturalistic-driving-studies:) the data are available through the Virginia Tech Transportation Institute (VTTI), which conducted this study. You could try to contact someone at their naturalistic data center (http://www.vtti.vt.edu/facilities/data-center.html). Also, as there does seem to be an existing fatigue-related data set from the SHRP2 database, you might check to see if those data are available. See http://dx.doi.org/10.15787/VTT1/ORGK0V for the link to the data set description.