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 ($>1sigma$) 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.
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