We use the framework developed as part of the MESA Isochrones and Stellar Tracks (MIST) project to assess the utility of several types of observables in jointly measuring the age and 1D stellar model parameters in star clusters. We begin with a pedagogical overview summarizing the effects of stellar model parameters, such as the helium abundance, mass-loss efficiency, and the mixing length parameter, on observational diagnostics including the color-magnitude diagram, mass-radius relation, and surface abundances, amongst others. We find that these parameters and the stellar age influence observables in qualitatively distinctive, degeneracy-breaking ways. To assess the current state of affairs, we use the recent Gaia Data Release 2 (DR2) along with data from the literature to investigate three well-studied old open clusters---NGC6819, M67, NGC6791---as case studies. Although there is no obvious tension between the existing observations and the MIST models for NGC6819, there are interesting discrepancies in the cases of M67 and NGC6791. At this time, parallax zero point uncertainties in Gaia DR2 remain one of the limiting factors in the analysis of these clusters. With a combination of exquisite photometry, parallax distances, and cluster memberships from Gaia at the end of its mission, we anticipate precise and accurate ages for these and other star clusters in the Galaxy.
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