I have a feeling Patterson is digging deep into candidates background and this is what is "taking so long". You have to think he knew it was possible he would have to let Barnes go, so he was already thinking about "who?" He also doesn't want to be embarrassed by a coach who may have skeletons like a falsified resume, etc. It's a mess an institution like Texas would want to avoid.
Maybe he had names in his head and is vetting the more sincere candidates deeply. I'm guess I'm willing to give him the benefit of the doubt at this point. Why couldn't the search take a week or 10 days, even if he's zeroed in on someone already?
I'll end this with the usual "what the hell do I know?" cuz I'm spitballin this entire post.