I think this is one of those things that only you can answer. I mean, everything is, in the end, but there is just so much nuance to stuff like this.

Your father reminds me of my father in a lot of ways-- they share some of those bullet points and are about the same age.

I go back and forth with mine. Right now I am just over a year of having no contact with him-- so given what you wrote, I would not call. He didn't call you on your birthday - why should you call him on his? Not to be petty or anything, but isn't he demonstrating that birthdays aren't important to him when he does that? Mine does the same thing, btw - and he will even get both the birthday and the child wrong.

In the past, I have gone through years where I do have contact because I worry that he will die and I will feel bad if I don't maintain some kind of relationship -- but, for me, I am at the point where I have given up. My father is incapable of having a relationship that isn't 100% about him and his wants.

If an email feels right to you, do that. If you don't want to acknowledge his birthday at all, you don't owe him anything.

Just curious -- would your father notice if you didn't say anything? Mine gets really upset if we don't acknowledge him, which just makes me roll my eyes given how he treats his kids.