Northern Irish Father, can I claim Irish Citizenship

I have come here because any Google search or attempt for me to find any sort of answer hasn't been completely cut or dry. My father was born in Belfast in 1950. As such he had a right to claim and Irish Passport and or a British one. However my father joined the RAF in 1967 and as such got his first passport and due to joining the RAF it was British.
My father has never bother or particulary cared about getting his Irish Passport as it was never any different to having a British one really. He now lives in America and thus as even less of a use to get one.
Question one. As my father was born in "Ireland" at least enough of it to be able to get an Irish passport anyway, could I still apply for Irish citizenship?
Question two. If that would work if I got him to get an Irish passport would that help?
Thank you.

My father was born in Belfast in 1950

You don’t need to ‘apply’ for citizenship. You are automatically an Irish citizen by descent. You can apply for a passport right away (and you can do this online if you now live in the EU/UK). Just make sure you can still find his birth certificate.

Whether he possesses an Irish passport today is irrelevant.

I suspect it’s always a pleasant surprise to learn that you can’t apply for Irish citizenship because you’re already an Irish citizen! As the previous poster pointed out, all you need is a passport.