I think it's very sad that your dad is insenstive to your needs. That must feel pretty bad. :-( . Obviously you want a relationship with him. If you have made that clear, I don't think there is anything more you can do on your part. I don't blame you at all for being reserved in continuing to send him your regards on his birthday. You are the only one that can decide that. I like your signature which says.. Listen to yourself, believe in yourself, and accept what it! That says a lot. Maybe you are at a place of letting go of the expectations you have for your dad to do what you want him to do. And perhaps you are allowing yourself to do what you think is right for you. And, you won't feel guilty for doing this or feel you aer doing it for pay back or spite. From your post, it doesn't sound like you are like that.
Can you ask you sister to do what she wants to do and let you decide for yourself what is right for you? Does he send greetings to her on her birthday?
Just some things to think about
"Hope is seldom found in the things we can see;it is the sweet fragrance of grace."