  Third-order galaxy-galaxy lensing (G3L) is a next generation galaxy-galaxy
lensing technique that either measures the excess shear about lens pairs or the
excess shear-shear correlations about lenses. It is clear that these statistics
assess the three-point correlations between galaxy positions and projected
matter density. For future applications of these novel statistics, we aim at a
more intuitive understanding of G3L to isolate the main features that possibly
can be measured. We construct a toy model ("isolated lens model"; ILM) for the
distribution of galaxies and associated matter to determine the measured
quantities of the two G3L correlation functions and traditional galaxy-galaxy
lensing (GGL) in a simplified context. The ILM presumes single lens galaxies to
be embedded inside arbitrary matter haloes that, however, are statistically
independent ("isolated") from any other halo or lens position. In the ILM, the
average mass-to-galaxy number ratio of clusters of any size cannot change. GGL
and galaxy clustering alone cannot distinguish an ILM from any more complex
scenario. The lens-lens-shear correlator in combination with second-order
statistics enables us to detect deviations from a ILM, though. This can be
quantified by a difference signal defined in the paper. We demonstrate with the
ILM that this correlator picks up the excess matter distribution about galaxy
pairs inside clusters. The lens-shear-shear correlator is sensitive to
variations among matter haloes. In principle, it could be devised to constrain
the ellipticities of haloes, without the need for luminous tracers, or maybe
even random halo substructure. [Abridged]
