From geodesic motion of photons to Maxwell equations in curved spacetime

In curved spacetime, 1.) a photon is supposed to move along a null-geodesic, i.e., a trajectory $x^{mu} = x^{mu}(lambda)$ satisfying $$frac{d^{2}x^{rho}}{dlambda^2} + Gamma^{rho}{}_{munu}frac{dx^{mu}}{dlambda}frac{dx^{nu}}{dlambda} = 0$$ and $$g_{munu}frac{dx^{mu}}{dlambda}frac{dx^{nu}}{dlambda} = 0$$ in conjunction, for some parameter $lambda$, while 2.) the source free Maxwell equations are given by $$nabla_{mu}F^{munu} = partial_{mu}F^{munu} + Gamma^{mu}{}_{rhomu}F^{rhonu} = 0.$$ The former generally depends on all 40 components of the Christoffel connection, while the latter depends only on 4 degrees of freedom of the Christoffel connection (its trace). My question is therefore the following:

Considering, loosely speaking, an electromagnetic wave to be a collection of photons, how can the latter be derived, in some limit(?), from the former? How do most of the degrees of freedom of the Christoffel connection get ‘washed out’ in any such process? By some averaging or what?

Does the Ricci tensor in the de Rham wave operator figuring in the equations of motion of the electromagnetic four-potential itself perhaps play a role, even though it is of second differential order in the metric whereas the Christoffel symbols are only of first order? I have no idea.

I would appreciate any hint or some reference to relevant literature.