Sry2Say but Fight Club is the purest Beta movie I have ever seen. IEIs are all head over heels for Tyler after they watch it. Where the heck are you seeing Te? Just because he has a lot of facts doesn't mean he doesn't have strong - look @ the functions together and what Tyler obviously values.
It would be laughable to even consider him dual seeking - check out what he does. He bands people together collectively, as one unit, without names! Everyone shaves their head, they are degraded, but in an way, it's all baby. Not LIE by a long shot. He values / ... the whole movie is about that. Imposing a structure (SeTi) ... he's a natural leader, knows how to rally troops and such.
I am also doing this for my film studies assignment (the biggest presentation ever) and I know a lot more about Fight Club now than I did before. Still love it, but I think Taxi Driver is a better film for what they're trying to convey.
Anyhow... Cornelius? I thought his name was Jack! Wow, is it? =/ Anyway I think he is an LII. He is so in need of some it's not even funny. But it's kinda strange how he does accept Tyler's imposement of on him ... it hurts him so bad (acid on hand lol) but in the end, he falls prey to it.