Galaxy clusters, occupying the most massive halos, serve as key laboratories for halo gas physics and galaxy evolution, hosting multiphase gas that contains clues as to how these environments have transformed over time. Accretion shocks are uniformly predicted in formation models of the intracluster medium (ICM), but their location (1-5 r200) varies from model to model, with important implications for infalling galaxies and gas physics in cluster outskirts. I am conducting a novel experiment to detect these accretion shocks through UV absorption spectroscopy of background quasars probing foreground galaxy clusters. The experiment works as follows: the accretion shock front heats infalling gas, which ionizes these gas clouds to a greater degree than photoionization in the intergalactic medium (IGM), and once the gas is exceedingly shock-heated, the neutral fraction should plummet, causing mappable depressions in the incidence of neutral hydrogen (H I) absorbers per unit redshift, dN/dz. Using HST/COS spectra, we select a statistical sample of quasar sightlines that probe 20 foreground galaxy clusters from within r200 to 5 r200 pairs, and quantify dN/dz as a function of projected clustocentric distance. My results reveal a peak around 3 r200, with an increase in the amount of absorption lines per sightline detected around the outermost accretion shock, indicating a buildup of infalling H I clouds just outside the outer accretion shock.