Photometric observations of accreting, low-mass, pre-main-sequence stars (i.e., Classical T Tauri stars; CTTS) have revealed different categories of variability. Several of these classifications have been linked to changes in $\dot{M}$. To test how accretion variability conditions lead to different light-curve morphologies, we used 1D hydrodynamic simulations of accretion along a magnetic field line coupled with radiative transfer models and a simple treatment of rotation to generate synthetic light curves. We adopted previously developed metrics in order to classify observations to facilitate comparisons between observations and our models. We found that stellar mass, magnetic field geometry, corotation radius, inclination, and turbulence all play roles in producing the observed light curves and that no single parameter is entirely dominant in controlling the observed variability. While the periodic behavior of the light curve is most strongly affected by the inclination, it is also a function of the magnetic field geometry and inner disk turbulence. Objects with either pure dipole fields, strong aligned octupole components, or high turbulence in the inner disk all tend to display accretion bursts. Objects with anti-aligned octupole components or aligned, weaker octupole components tend to show light curves with slightly fewer bursts. We did not find clear monotonic trends between the stellar mass and empirical classification. This work establishes the groundwork for more detailed characterization of well-studied targets as more light curves of CTTS become available through missions such as the Transiting Exoplanet Survey Satellite (TESS).