I don't think that "Timbuktu" is "nonsensical". I took it to indicate the father was of African
descent, that is, he was a black man.

Taconicus, what do you think of this:

I was born in Arkansas, where my mammy met my pa.
Pappy hailed from Oklahoma City.
There's one thing I recall, that I hated most of all,
Was that little green shed, our privy.

"squaw" and "Timbuktu" are both gone, the neologism "craperoo" gets replaced by "privy",
which almost rhymes with "City". Not many words that rhyme with "privy".