Considering bisexuality and demi sexuality I suspect that attraction is what we are measuring, not just gayness. Perhaps even attraction along two dimensions - romantic and sexual. This has interesting implications considering that gender itself exists as a spectrum with multiple dimensions of its own, at very least expression and identity, perhaps sex should be incorporated too which further complicates matters...
Nonetheless, I don't believe that any of this precludes our units of attraction from being discrete... I will concede that it's probably more likely, if there is some kind of fundamental attraction particle, that it has comparable properties to the photon.
I'm considering that each of these attraction particles (furthermore referred to as attractons) exists as excitations in the gender/sexuality field. Thanks to wave particle duality we can have a quanta of attraction with continuous possible amounts of attraction associated with each - just like the photon's variable energy.