Most Helpful Guy
You guys are half broken up and half not broken up. The two of you need to talk and decide which one it is. You need to look at why you broke up in the first place and ask yourselves honestly what has changed. There must have been a reason. If that reason still exists, then you are fooling yourselves by continuing to act like you are still together. If your issues have been resolved, then decide if you really want to stay together. But the halfway in between relationship is just wasting both of your time.
This has nothing to do with a Christmas gift, this requires HONEST discussion. A gift can not win your ex back. Only words, actions and honesty can do that. You need to be honest with yourself and honest with each other. There is nothing wrong with giving him a Christmas gift. You just have to know if you are giving it to your boyfriend, "just" a friend, or something else. If you want to use the gift as some kind of symbol to show that you still care, and maybe lead to the type of discussion that you need, that's fine. Just don't let it replace that discussion.
As for what to get him, you know him better than us. If he likes art, just find something you think he'd like.
But please don't let the "atmosphere" of Christmas sway either of your thinking. A relationship lasts, the atmosphere of Christmas is fleeting. You need to know which one it is.