Uveal melanoma (UM) is the most prevalent cancer of the eye in adults, with a highly aggressive form of metastasis that is refractory to current therapies. UM is driven by aberrant activation of the Gαq pathway by hotspot activating mutation of GNAQ/GNA11, with few additional genetic aberrations. Despite this, there are limited effective targeted therapies currently available against the treatment of UM and mUM. Here, we performed a high-throughput chemogenetic drug screen in GNAQ-mutant UM contrasted with that of BRAF-mutant skin cutaneous melanoma, as a network chemical biology-based approach to identify therapeutic agents that target the mechanistic underpinnings driving UM. We observed strong genotype-driven drug sensitivities, and identified several drug classes with preferential activity against UM using a method termed Drug Set Enrichment Analysis (DSEA). Among them, we found an enrichment for PKC inhibitors, and identified one compound LXS-196, with the highest preferential activity against UM. Our investigation into the mechanism of action of LXS-196 revealed that in addition to inhibiting the Gq-ERK pathway, unlike other PKC inhibitors, this drug also reduced FAK activity, a recently identified mediator of non-canonical Gαq-driven oncogenic signaling. Kinome profiling revealed that LXS-196 acts as a multi-targeted kinase inhibitor, with high preference for PKC as well as PKN/PRK, the latter a poorly investigated AGC kinase that is activated directly by RhoA. This primes LXS-196 to target cell-essential pathways that drive tumor growth in UM by targeting both PKC, in addition to FAK. Moreover, we find that PKN is activated by GNAQ downstream from RhoA, thereby contributing to FAK stimulation. These findings expose a signaling vulnerability that can be targeted pharmacologically. Ultimately, dual PKC and PKN inhibition by LXS-196 acts synergistically with FAK inhibitors (FAKi) to halt UM growth and promote cytotoxic cell death in vitro and in preclinical metastatic mouse models, thus providing a highly translatable therapeutic multimodal precision strategy against mUM.