"Dingus", according to the OED, comes from Dutch via Afrikaans; from the quotations it seems that the plural dinges got transmogrified into mock Latin. But the OED is unaware that it also has the specialized meaning "dildo".

It is true that by & large, in IndoEuropean languages, grammatical gender is correlated with sex, but there are many exceptions, and there is no difficulty in applying a masculine noun to the female organ. Indeed, the actual vulgar Latin word, "cunnus", was masculine; and contrariwise the vulgar word for penis, "mentula", was feminine! One can imagine philologists arguing all night about that.

Slang words that can apply to both male and female genitals are rare, but "will" is an example in Elizabethan English; Shakespeare punned on it elaborately in one of his sonnets.