Ach Grrr - I feel your pain! Ds1 was very similar at 13, and I had to pull apart him and his younger brother a few times - he lived on planet 'meh'
. One minute he is screaming he is an adult, next minute, he is snuggled up... One day he sounds like Jeremy paxman with a grudge - next day he is loving...
It was hard work, and I had to shape-shift a few times to deal with it. Actually, it was a bit of a shock tbh - I had to rethink my parenting a bit - as parents we often think on our feet, but I had to spend some time thinking what is important, what messages am I sending him, where is he at, and about boundaries and values etc.
I know that makes me sound tossy..... sorry!
He's now 15 and a half, and much better - pretty lovely actually - picks his younger brother up from school when I am working till 4pm.
If his younger brother is having a hissy fit about his homework, and we are at loggerheads about it, he will lazily lie down on the sofa, and explain things to him - "Hey cool!! - we did it that way when I was in juniors, - why don't you try looking it like x,y, or z...."
Lo and behold it suddenly all makes sense to ds2..
and crisis is over - bloody hell!
He showers every day now, organises himself, can paint a wall and make meals etc...
He is doing some GCSE's a year early, and he comes home after the finish of biology - I get home from work "Hey! Ds1! how did the bio exam go?"
Ds1 (strumming his guitar) "yeah - Ok - thanks for asking.."
Me "But how did it go? was it hard, did you finish in time? did the questions come up that you were expecting? 
Ds1 - "yeah - whats for tea? - can 'J' come for a sleepover at the weekend?"
courage mes braves