Dear T.,
Although I don't have a big age difference between my two kids, I do have teens, so I hope this helps:
My son is going on 16 this June. Each year he pushes away from me more. It's the teen's way of seeking independence. Let him prove to you he can do it alone, but keep him responsible by expecting adult behavior from him. He'll appreciate your allowing him to prove himself capable of being an adult, which will bring him closer to you. Don't forget the Kudos for those times when you find out he can do it alone. He needs to hear those too. (even if he rolls his eyes)
My son, especially this year, has been mocking me, and pulling away. He corrects me like I'm stupid. He doesn't want to be "seen" as a "momma's boy" to his friends. It's embarassing to him. He's trying to grow up, so I'm allowing him this by curbing my desire for close affection(especially in front of friends). He lets me give him a hug now and then. And I thank him for that. Usually no friends are around. He hates when I baby him, or lecture him anymore. He feels he knows it all. And although I know he doesn't, from now on if he doesn't let me lecture to him, he's on his own with his results. I hold him to his word that he can do this. For example; if he gives me a hard time about telling him how to do something and he fails at it I get the joy of calmly saying, well, if you had come to me for advice I could have told you that, but you know it all so you don't need my advice it seems. Or even nicer I just say, well dude, live and learn.
But as a parent I still have to put my foot down and keep the ground rules. Until he moves out there will be rules in the house that he must abide by. Luckily, so far, he doesn't push that envelope (yet).
My daughter however, is turning out to be more of a pill. She's going on 15. They are 14 months apart and night and day in comparison. But in her case, it's the "boyfriend" issues. Staying on the phone too much, wanting to see him every minute, driving us crazy asking for a ride or for him to come over when daddy really dislikes this boy. (typical dad) The boy is, however, very disrespectful so I must agree this time. But she is in "love" so it's hard to say no. We do our best to curb her infatuation, keep them from being alone for long periods of time, and chaperone them to the movies, but from a distance. It's tricky to be their friend and their parent but I have to keep the communication open so I try to keep up on their ups and downs. Try to help them through what to them seems like a major issue when to us it's only puppy love.
Anyway, yes, 13 is when it starts. You'll see him grow a lot too. Jeff was really very moody through this time, his voice has changed, he got taller so fast. He was two inches shorter than his younger sister in 6th grade, but by 9th grade he grew to two inches taller than her! We were getting worried he wouldn't grow taller since a lot of boys were taller than Jeff sooner. He's now my little man. Sounds like his dad on the phone, and really hates open affection from me. I got a hug last night before bed. That felt nice. He has a little mustache coming on as well as peach fuzz on his chin. I get melencholy remembering my little IMP toddler. He loved his mommy so much. I know he still does but it's still hard to lose that open affection. He is now 5'8" and she's 5'6" I am only 5'4" so I'm the shorty around here. It really feels weird to have my kids outgrow me.
Hang in there. He's normal. Love from a distance. Maybe giving him some adult duties, like helping you with the baby at times, babysitting, etc... will help keep the bond tighter. And if he does a good job, you get to give him a nice hug and he will most likely allow that. ;) You both win!
Hugs! ;)