Gamma-Ray Infrastructure For Fundamental Investigations of Nuclei (GRIFFIN) is a new high-efficiency γ-ray spectrometer designed for use in decay spectroscopy experiments with low-energy radioactive ion beams provided by TRIUMF's Isotope Separator and Accelerator (ISAC-I) facility. The high-efficiency GRIFFIN array comprises 16 Compton-suppressed large-volume HPGe clovers, and is designed to be used with a suite of ancillary detectors, providing a powerful and versatile tool for studying exotic nuclei. The structures of N=82 nuclei below doubly-magic 132Sn are crucial for calculations of the astrophysical r-process as these isotopes form 'waiting-points' that play an important role in the formation and shape of the second r-process abundance peak. Many of the most neutron-rich N=82 nuclei are, however, out of reach to the current generation of radioactive beam facilities and their properties must be predicted. In the past, shell-model calculations for the half-lives of these nuclei have been performed by adjusting the quenching of the Gamow-Teller (GT) operator in order to reproduce the half-life of 130Cd. However, the calculated half-lives of the nuclei below 130Cd are known to be systematically too large. A recent measurement of the 130Cd half-life with EURICA indicated a shorter half-life of 130Cd, which would lead to a re-scaling of the GT quenching by a constant factor for all nuclei in the region and potentially resolves the discrepancy. However, the reduced quenching of the GT operator implied by these results creates a new discrepancy in the calculated half-life of the N=82 isotope 131In. Half-life measurements of nuclei in this region are complicated due to the presence of β-decaying isomers with comparable half-lives and large βn branches, making γ-ray photo-peak gating with a high-resolution, high-efficiency, γ-ray spectrometer an ideal method to measure each of the isomeric half-lives. In this work, measurements of the half-lives of the 128−130Cd isotopes were performed. The half-life of the N=82 r-process waiting point nucleus 130Cd was measured to be 126(4)~ms confirming the EURICA measurements and in strong disagreement with the earlier measurements of 162(7)~ms and 195(35)~ms. A detailed data set for the β and βn decay of 131In was also analyzed. The β decay from the single proton hole nucleus 131In to the single neutron hole nucleus 131Sn is of current interest with respect to advancing our understanding of nuclear forces and shell evolution in this region, including modelling the astrophysical r-process. In this work, three different β decaying states in 131In were studied in detail, providing new information about the shell structure of 131Sn. The half-lives of these three β decaying states of 131In measured in this work agree with the previous measurements. The half-life of each β decaying state of 131In is significantly longer than the half-life predicted from shell-model calculations.