Measuring presence is critical to improving user involvement and performance in Mixed Reality (MR). \emph{Presence}, a crucial aspect of MR, is traditionally gauged using subjective questionnaires, leading to a lack of time-varying responses and susceptibility to user bias. Inspired by the existing literature on the relationship between presence and human performance, the proposed methodology systematically measures a user's reaction time to a visual stimulus as they interact within a manipulated MR environment. We explore the user reaction time as a quantity that can be easily measured using the systemic tools available in modern MR devices. We conducted an exploratory study (N=40) with two experiments designed to alter the users' sense of presence by manipulating \emph{place illusion} and \emph{plausibility illusion}. We found a significant correlation between presence scores and reaction times with a correlation coefficient -0.65, suggesting that users with a higher sense of presence responded more swiftly to stimuli. We develop a model that estimates a user's presence level using the reaction time values with high accuracy of up to 80\%. While our study suggests that reaction time can be used as a measure of presence, further investigation is needed to improve the accuracy of the model.