  We consider the redshift drift and position drift associated with
astrophysical sources in a formalism that is suitable for describing emitters
and observers of light in an arbitrary spacetime geometry, while identifying
emitters of a given null-geodesic bundle that arrives at the observer
worldline. We then restrict the situation to the special case of a
Lemaitre-Tolman-Bondi (LTB) geometrical structure, and solve for light rays
propagating through the structure with arbitrary impact parameters, i.e., with
arbitrary angles of entry into the LTB structure. The redshift drift signal
emitted by comoving sources and viewed by a comoving observer turns out to be
dominated by Ricci curvature and electric Weyl curvature contributions as
integrated along the connecting light ray. This property simplifies the
computations of the redshift drift signal tremendously, and we expect that the
property extends to more complicated models including Swiss-cheese models. When
considering several null rays with random impact parameters, the mean redshift
drift signal is well approximated by a single Ricci focusing term. This
suggests that the measurement of cosmological redshift drift can be used as a
direct probe of the strong energy condition in a realistic universe where
photons pass through many successive structures.
