It wouldn't surprise me at all if one or more B1G teams played a Friday night game considering the Conference started in 1896 and the night game era began in the late 1920s. Most likely, though, it would have been a contest not held at a B1G field.
On October 5, 1900 Drake University defeated Grinnell College 6-0 under arc lighting in the first complete, college outdoor night game held in Des Moines, Iowa according to the next day’s Des Moines Register and Leader.
October 11, 1930 saw the first night college football games in Manhattan, Brooklyn and Washington, D.C. according to the next day’s New York Herald-Tribune. Manhattan met Oglethorpe in front of 18,000 at the Polo Grounds. St. John’s of Brooklyn met Niagara at Dexter Park before 7,000. They also used a white football. And Georgetown played West Virginia Wesleyan at Griffith Stadium with 15,000 in attendance.