The program covering the August 25, 1996 event does not list the non-qualifiers in the race report. Nor does that week's AARN, which I have a copy of handy (I don't have the issues for the earlier part of '96 handy.)
Both are essentially the same article and mention 38 cars on hand. Based on the pictures and text, among the 12 non-qualifiers are Josh Pannepacker, Scott Lutz, Charlie Firestone, and Steve Delliponti. No idea who the other 8 were.