  A small subset of young stellar objects (YSOs) exhibit "see-saw" temporal
variations in their mid-infrared SED; as the flux short-ward of a fulcrum
wavelength ($\lambda_{f}$) increases the flux long-wards of this wavelength
decreases (and vice-versa) over timescales of weeks to years. While previous
studies have shown that an opaque, axisymmetric occulter of variable height can
cause this behaviour in the SED of these objects, the conditions under which a
single $\lambda_{f}$ occurs have not previously been determined, nor the
factors determining its value. Using radiative transfer modelling, we conduct a
parametric study of the exemplar of this class, LRLL 31 to explore this
phenomenon, and confirm that the cause of this flux variation is likely due to
the change in height of the optically thick inner rim of the accretion disc at
the dust sublimation radius, or some other phenomenon which results in a
similar appearance. We also determine that a fulcrum wavelength only occurs for
high inclinations, where the line of sight intersects the accretion disc.
Accepting that the disc of LRLL 31 is highly inclined, the inner rim radius,
radial and vertical density profiles are independently varied to gauge what
effect this had on $\lambda_{f}$ and its position relative to the silicate
feature near $10 \mu$m. While $\lambda_{f}$ is a function of each of these
parameters, it is found to be most strongly dependent on the vertical density
exponent $\beta$. All other factors being held constant, only for flatter discs
($\beta < 1.2$) did we find a $\lambda_{f}$ beyond the silicate feature.
