Exploring citizenship - eligibility questions

Hi all,

I’m starting to look into whether a German passport/dual citizenship is possible for me as an American. For context:

-Paternal grandmother was born in Germany in the late 1930s -Father was born in Germany in the late 1950s. He was born in a small village so I’m not sure what paperwork may exist from then, though his birthplace is listed in his obituary -Father and grandmother immigrated to the US at some point in the 1960s -Father joined the US military in the 1970s - I was always told that he had to renounce his German citizenship to join, though I don’t know if that’s true? I’m pretty sure he naturalized as a US citizen at some point however -My American mother and German father were married when I was born in the 1990s. They later divorced.

My father unfortunately passed in my teens and I wasn’t able to appreciate that I may need some of his paperwork. I’m in the process of attempting to retrieve what I can from my paternal grandmother but it’s not 100% clear what she’s in possession of. Hoping to get more clarity on that during holiday visits.

Would I be eligible for citizenship, and is it worth pursuing with the information I have available? There is a German embassy in my city. Thank you in advance for any guidance.