There's no reason at all to think it's a wig. It's just an unusual haircut. The video on Tw*tter is not 'proof', and diagnosing him as having a thyroid problem is ridiculous.

Some people seem to think that other people's comments on here are a bona fide window on the world! Well they aren't.
Also, it's okay if you don't like the way he talks or acts, but having decided that you don't like him it's rather puerile to slate his physical appearance. I'm not talking about his haircut - if you want to ridicule him for his fashion choices I suppose that's fair game - but berating him for having a wonky eye? Seriously?
Thom Yorke of Radiohead fame has a similarly wonky/half-closed eye. I wonder how many people happily overlook that fact, rather than pointing it out? There's a reason that pointing out other people's imperfections is normally consigned to the schoolyard, and that's because most people during the course of their life will meet an imperfect person who they like and realize the meaning of 'superficial'.