Several independent groups have pursued and realized the creation of modern SII instruments to perform high angular resolution observations at optical wavelengths, one such instrument being VERITAS-SII (Very Energetic Radiation Imaging Telescope Array System with Stellar Intensity Interferometry). An analysis methodology customized for signal extraction of VERITAS-SII data is presented. Systematics which effect the measured instrumental sensitivity are explored and subsequently corrected for. An observationally driven statistical framework is implemented to perform Bayesian inference with a uniform disk squared visibility model, subsequently measuring the instrumental sensitivity of the VERITAS-SII system with VERITAS-SII data taken of Eta UMa on December 20th, 2021. The statistical framework is expandable to more complex squared visibility models like limb darkened uniform disk and binary models. The sensitivity measurement presented can be used to extrapolate the sensitivity limitations of the VERITAS-SII instrument and future SII instruments.