I think I would start with your birth certificate, which will give the place of birth of your father, as well as the name and birth information of your mother.
You can get a copy from Arizona Health Services in Phoenix.
If he was born in Arizona, you can then go to AHS and get a copy of his birth certificate, which will have his parents' names. Likewise with mother. Your mother's death certificate may or may not be of help, but I'd ask anyway. If you're in Phoenix, I'd make a personal trip. Take identification.
You can also get Grace's Death Certificate, which may be this:
Name: Gracie Ishmael
SSN: 494-30-5423
Born: 7 Aug 1930
Last Benefit: 85024 Phoenix, Maricopa, Arizona, United States of America
Died: Aug 1984
State (Year) SSN issued:
Missouri (Before 1951)
If you are involved with the medical community, ask for a social worker. They can get through walls the rest of us cannot.
Hope this helps.
Pat