Just realized I am missing some times for 1998-2000. I will limit it to 2001 to present. Games started at 41 different times. Found some other errors but the conclusion is the same.
Games starting between 4 and 410pm: 23-14, average 18,021
Games starting between 6 and 610pm: 32-12, average 20,677
Here is the list
2001 Nicholls State W 2:00 p.m. Saturday 13707
2001 Southern Mississippi L 5:00 p.m. Saturday 14132
2001 Middle Tennessee L 7:00 p.m. Saturday 12102
2001 UL Monroe W 4:00 p.m. Saturday 17353
2001 New Mexico State L 2:00 p.m. Saturday 9321
2002 Minnesota L 7:00 p.m. Saturday 20512
2002 UAB W 6:00 p.m. Saturday 19616
2002 North Texas L 4:05 p.m. Saturday 8413
2002 Idaho W 4:00 p.m. Saturday 12621
2002 Arkansas State W 4:00 p.m. Saturday 14117
2003 Louisiana Tech L 7:00 p.m. Saturday 24211
2003 Houston L 7:37 p.m. Saturday 11127
2003 UL Monroe L 4:00 p..m. Saturday 13540
2003 New Mexico State W 6:05 P.M. Thursday 12308
2003 Idaho W 4:00 p.m. Saturday 9213
2003 Florida International W 4:00 p.m. Saturday 13571
2004 Northwestern State W 7:00 P.M. Saturday 22117
2004 Middle Tennessee W 6:07 p.m. Saturday 25083
2004 Arkansas State W 4:05 p.m. Saturday 23121
2004 North Texas L 9:20 p.m. Friday 21608
2004 Troy L 2:36 p.m. Saturday 15077
2005 Northwestern W 7:05 p.m. Saturday 17,341
2005 UCF L 7:00 p.m. Saturday 18,262
2005 Florida Atlantic L 7:05 p.m. Thursday 14,208
2005 Troy W 4:00 p.m. Saturday 21,204
2005 Florida International W 6:07 p.m. Saturday 16,942
2006 North Carolina A&T W 4:45 p.m. Saturday 15,041
2006 Eastern Michigan W 4:00 p.m. Saturday 15,923
2006 Middle Tennessee L 4:00 p.m. Saturday 21,485
2006 North Texas L 4:00 p.m. Saturday 13,621
2006 Arkansas State W 4:00 p.m. Saturday 10,212
2006 UL Monroe L 4:00 p.m. Saturday 10,814
2007 Ohio L 6:00 p.m. Saturday 22,186
2007 McNeese State L 6:00 p.m. Saturday 33,828
2007 Troy L 6:00 p.m. Saturday 14,091
2007 North Texas W 6:00 p.m. Saturday 9,464
2007 Florida Atlantic L 4:08 p.m. Saturday 12,290
2007 UL Monroe L 6:00 p.m. Saturday 8,045
2008 Kent State W 6:00 p.m. Saturday 18,241
2008 Arkansas State W 6:00 p.m. Saturday 23,684
2008 Florida International W 4:00 P.M. Saturday 29,031
2008 UT El Paso L 6:08 p.m. Saturday 21,065
2008 Middle Tennessee W 6:08 p.m. Wednesday 15,321
2009 Southern University W 6:00 p.m. Saturday 41,357
2009 Kansas State W 6:02 p.m. Saturday 16,431
2009 North Texas W 6:07 P.M. Saturday 12,141
2009 Florida Atlantic L 4:00 p.m. Saturday 21,135
2009 UL Monroe W 6:00 p.m. Saturday 8,689
2009 Troy L 6:00 p.m. Saturday 12,245
2010 Arkansas State W 2:30 p.m. Saturday 15,103
2010 Middle Tennessee L 6:00 p.m. Saturday 17,249
2010 Oklahoma State L 8:05 p.m. Friday 25,881
2010 Western Kentucky L 4:00 p.m. Saturday 15,641
2010 Florida International L 6:00 p.m. Saturday 13,041
2011 Nicholls State W 6:08 p.m. Saturday 28,741
2011 Florida Atlantic W 6:08 p.m. Saturday 26,339
2011 Troy W 6:04 P.M. Saturday 29,775
2011 North Texas W 4:08 p.m. Saturday 32,823
2011 UL Monroe W 2:39 p.m. Saturday 28,176
2012 Lamar W 6:08 p.m. Saturday 25,803
2012 Florida International W 6:04 p.m. Saturday 21,109
2012 Tulane W 4:07 p.m. Saturday 29,758
2012 Arkasnas State L 7:01 P.M. Tuesday 19,873
2012 Western Kentucky W 6:04 p.m. Saturday 20,314
2012 South Alabama W 4:07 p.m. Saturday 20,333
2013 Nicholls W 6:04 p.m. Saturday 28,871
2013 Texas State W 6:04 p.m. Saturday 23,108
2013 New Mexico St. W 4:04 p.m. Saturday 30,028
2013 Troy W 6:32 P.M. Thursday 22,562
2013 UL Monroe L 6:06 P.M. Saturday 25,309
2014 Southern U. W 6:04 P.M. Saturday 36,170
2014 Louisiana Tech L 6:04 p.m. Saturday 25,607
2014 Georgia St. W 6:04 p.m. Saturday 24,616
2014 Arkansas St. W 7:04 p.m. Tuesday 21,760
2014 South Alabama W 4:05 P.M. Saturday 25,861
2014 App State L 1:04 p.m. Saturday 20,638
2015 Northwestern St. W 6:05 p.m. Saturday 26,824
2015 Akron L 6:04 P.M. Saturday 24,679
2015 Texas St. W 6:05 p.m. saturday 21,377
2015 UL Monroe W 4:05 p.m. Saturday 17,410
2015 New Mexico St. L 4:04 p.m. Saturday 17,023
2015 Troy L 4:05 p.m. Saturday 22,264
2016 Boise St. L 11:06 a.m. Saturday 22,661
2016 McNeese W 6:05 p.m. Saturday 26,891
2016 South Alabama W 6:05 p.m. Saturday 19,208
2016 App State L 7:05 p.m. Wednesday 16,960
2016 Idaho L 4:04 p.m. Saturday 21,387
2016 Arkansas St. W 11:06 a.m. Saturday 14,259
2017 Southeastern Louisiana W 6:05 p.m Saturday 18,289
2017 UL Monroe L 4:05 p.m. Saturday 18,318
2017 Texas St. W 6:32 p.m. Thursday 13,106
2017 New Mexico St. W 4:05 p.m. Saturday 16048
2017 Ga. Southern L 4:05 p.m. Saturday 12993
2018 Grambling W 6:06 p.m. Saturday 28866
2018 Coastal Carolina L 6:05 p.m. Saturday 17125
2018 New Mexico St. W 4:05 p.m. Saturday 18131
2018 Arkansas St. W 6:05 p.m. Saturday 17068
2018 Georgia St. W 4:05 p.m. Saturday 14945
2018 South Alabama W 4:05 p.m. Saturday 15168
2019 Liberty W 6:35 p.m. Saturday 16,231
2019 Texas Southern W 6:35 p.m. Saturday 18,183
2019 App State L 7:05 p.m. Wednesday 20,012
2019 Texas St. W 4:06 p.m. Saturday 21,063
2019 Troy W 4:05 p.m. Saturday 14,262
2019 UL Monroe W 6:33 p.m. Saturday 14,227
2020 Ga. Southern W 11:01 a.m. Saturday 5,585
2020 Coastal Carolina L 6:35 p.m. Wednesday 5,585
2020 Arkansas St. W 11:02 a.m. Saturday 5,585
2020 South Alabama W 1:06 p.m. Saturday 5,585
2021 Nicholls W 6:04 p.m. Saturday 25,417
2021 Ohio W 7:05 p.m. Thursday 17,709
2021 App State W 6:35 p.m. Tuesday 20,066
2021 Texas St. W 11:02 a.m. Saturday 28,794
2021 Georgia St. W 6:36 p.m. Thursday 16,007
2021 ULM W 3:02 p.m. Saturday 18,447
2022 Southeastern Louisiana W 6:03 p.m. Saturday 16,812
2022 Eastern Michigan W 6:04 p.m. Saturday 18,079
2022 South Alabama L 4:02 p.m. Saturday 20,671
2022 Arkansas State W 4:03 P.M. Saturday 15,017