I have a brother who is nearly ten years younger than I am. We have a good relationship, but the biggest mistake that I and my older brothers made was to think our youngest brother needed another parent. He didn't. Unsolicited advice from a much-older sibling is even less welcome than advice from one near your own age, because you know this much: Much-older siblings never ask for advice from the younger ones! I didn't learn until we were both adults is that what my younger brother needed most from me is to have me listen and be absolutely discrete and non-judgemental about what I heard. If I did give advice, I learned to put it in the form of "well, since you're asking, one way to look at it is this...other people I know do this....I've had the best luck with this..." Then let him decide what he decides, and if you think it's the wrong decision, bite your tongue. If he wants your opinion, he'll ask for it. If you expect him to always do what you advise, he won't ask again.
Also, if he is a boy, he isn't going to want to have a relationship by talking. He's going to want to have a relationship by doing. If you want to have a relationship with him, then, be there to help him do things that he couldn't do if you weren't there, and do it in a way that your parents don't. You may do with him about 1,000 times more than you ever talk with him. That's OK. It is the 1,000 times of doing that will even get you on the radar as someone he would dream of talking to.
So I would do this: "Jon, you know what? I finally realized something. I've been treating you as if I'm your mom, not your sister. That's kind of silly, because you already have a great mom, and a great dad."
Can we start over? I'd like to do stuff with you, just to be doing stuff together. I'd like to learn to listen like a sister, too, and not like your mom...which is to say, to not give any advice or tell you what I think unless you ask. Could we do that? Because someday when Mom and Dad are old and we have to take care of them, I'd like to know that you and I know each other, and we had fun together when we had the chance. Besides, I don't think I ever told you this, but I think you're going to be a really outstanding man. I want to spend time with you, starting right now. When we're both older, I think that's going to be something we're going to want to have done."
Then let him tell you what he wants to do, even if that is learning how to play video games. If you say, "I don't like video games", that is OK, but "I don't like video games, except with you" is even better. If he's a baseball player, take him to the batting cages...and just let him bat. No advice. Most of all, encourage him to tell you if he would like to do things differently.
Oh, and if you can think of a decision you have to make that you would be willing to leave up to him, ask him. Give him two options, both of which you are willing to do, then do what he suggests. Let him know how it worked out, and thank him for being willing to let you know his thoughts. This is a gift that most very-much-younger brothers rarely get.