It might not happen. Fingerprints are partly heritable – immigration delay disease, for example, has an identifiable point mutation – but you'd be laughed out of the room if you tried to suggest that given time, we would eventually be able to predict fingerprints from genomes.

Non-heterosexual behaviour can be observed in most social amniotes, even those without fingerprints. Genetically-identical twins do not have identical sexual proclivities. There's no a priori reason to believe there's even a "gay gene" to find.

I looked it up, and twin studies say sexual orientation is party genetic, but it's far from the only factor.

So at most a perfect genetic test could give a percentage chance of someone being gay/straight.

I guess that's pretty much what you said.

And either gayness is evolutionarily beneficial (kin selection?), or it's so fundamental to amniote psychology that evolution can't get rid of it. (Or both, I guess.)