  We present a phenomenological forward Monte Carlo model for forecasting the
population of active galactic nuclei (AGNs) in dwarf galaxies observable via
their optical variability. Our model accounts for expected changes in the
spectral energy distribution of AGNs in the intermediate-mass black hole (IMBH)
mass range and uses observational constraints on optical variability as a
function of black hole (BH) mass to generate mock light curves. Adopting
several different models for the BH occupation function, including one for
off-nuclear IMBHs, we quantify differences in the predicted local AGN mass and
luminosity functions in dwarf galaxies. As a result, we are able to model the
variable fraction of AGNs as a function of physical host properties, such as
host galaxy stellar mass, in the presence of complex selection effects. We find
that our adopted occupation fractions for the "heavy" and "light" initial BH
seeding scenarios can be distinguished with variability data at the $2-3
\sigma$ level for galaxy host stellar masses below $\sim 10^8 M_\odot$ with the
Vera C. Rubin Observatory. We demonstrate the prevalence of a selection bias
whereby recovered IMBH masses fall, on average, above the predicted value from
the local host galaxy - BH mass scaling relation with the strength of the bias
dependent on the survey sensitivity. The methodology developed in this work can
be used more broadly to forecast and correct for selection effects for AGN
demographic studies in synoptic surveys. Finally, we show that a targeted
$\sim$ hourly cadence program over a few nights with the Rubin Observatory can
provide strong constraints on IMBH masses given their expected rapid
variability timescales.
