  Even with several thousand {\it Fermi}-LAT blazar detections, the
$\gamma$-ray emission mechanism is poorly understood. We explore correlated
optical/$\gamma$-ray flux variations for 178 {\it Fermi}-LAT blazars regularly
monitored by KAIT, SMARTS, and the Steward Observatory. Out of the 178 sources,
121 show a measurable ($>1\sigma$) discrete correlation function peak. Using
the derived time-lags and Bayesian block light-curve decompositions, we measure
the fraction of common and orphan flares between the two bands. After
accounting for sampling and sensitivity limitations we quantify for the first
time the true orphan flare rates of optical and $\gamma$-ray flares: 54.5\% of
optical and 20\% of $\gamma$-ray flares are orphan events. Both the intraband
temporal relation and the small orphan $\gamma$-ray flare fraction point toward
leptonic processes as the likely mechanism for the high-energy emission.
Motivated to discriminate between synchrotron self-Compton and external-Compton
dominance in individual sources, we use the flux-flux variations to determine
the slope $m$ of the ${\rm log}\,f_{\rm opt} - {\rm log}\,f_{\gamma}$
dependence. The slope distribution suggests a bimodal population with high and
intermediate synchrotron-peak objects showing larger $m$ than low
synchrotron-peak objects. We find that $m$ is naturally decreased through
pollution from the orphan (typically optical) flares and develop a method to
statistically recover, given the sources' measured orphan flare rate, the
intrinsic $m$. While source classes show composite behavior, the majority of BL
Lac objects favor $m=2$, indicating a synchrotron self-Compton origin for the
$\gamma$-rays. No preference for either $m$ is found in flat spectrum radio
quasars.
