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.