Oh definitely he is wanting to see more of you and you have to be congratulated for your patience to get to this point.
If you want to do something for his birthday without appearing to pursue or anything, make it a casual event, anything, whether it be a day at the beach and casual dinner at home. By taking it slow and keeping it casual he won't be frightened off back into his tunnel (we don't want that to happen).
I am glad he is there more for the kids now especially your D, I do believe it is not just sons who need their fathers, daughters need them just as much and so this is great that he is back in their lives more now.
He will continue to come toward you Cas, it will be slow, but it will happen of that I am positive.