Don't think there's much to learn here:
At 1723, controller informed the pilot he was abeam YEAGR and requested the aircraft's fuel status, which the pilot reported as eight hours.
At 1814, the controller cleared the pilot to fly the RNAV GPS Runway 35 approach, which would be the sixth approach attempt. The pilot acknowledged the approach clearance and stated he was "getting tired of flying this airplane". The controller asked the pilot if there was anything he could do to help and if he would like to try a VMC airport. The pilot replied he would like to continue to attempt to land at HQZ and "keep working until we get it".
Data from the engine monitor was downloaded and plotted. The airplane's fuel flow of 27 gallons per hour (gph), consistent with takeoff power, was observed towards the start of the recording. A similar fuel flow was observed four times throughout the event flight at 17:10:42, 17:26:12, 18:00:24, and 18:07:48. At 18:13:12, the fuel flow dropped to an average of 7 gph, consistent with low power, for the duration of the recording.
On December 18, 2014, at 1816 central standard time, a Beech V35A airplane, N555SF, impacted terrain near Seagoville, Texas.
The refueling lineman stated that he added 16 gallons of fuel and was not able to visually sight any fuel in either main tank, consistent with about 44 gallons of fuel or less on board. Data from the engine monitor indicated that 44.4 gallons of fuel had been consumed at the time of the accident.
So, while the report's cover claims spatial disorientation in IMC as the reason for the loss of control, it turns out that, on the evening in question, the poor fellow couldn't fly an instrument approach of any sort, couldn't communicate how much fuel he had remaining, probably didn't know, and, whether his engine quit or not, he lost control with the tanks dry.