The Taurus-Auriga association and its associated molecular cloud are a benchmark population for studies of star and planet formation. The census of Taurus-Auriga has been assembled over seven decades and has inherited the biases, incompleteness, and systematic uncertainties of the input studies. The notably unusual shape of the inferred IMF and the existence of several isolated disk-bearing stars suggest that additional (likely disk-free) members might remain to be discovered. We therefore have begun a global reassessment of the membership of Taurus-Auriga that exploits new data and better definitions of youth and kinematic membership. As a first step, we reconsider the membership of all disk-free candidate members from the literature with spectral type $ge$F0, $3^h50^m<alpha<5^h40^m$, and $14^{circ}<delta<34^{circ}$. We combine data from the literature with Keck/HIRES and UH88/SNIFS spectra to test the membership of these candidates using HR diagram positions, proper motions, RVs, H$alpha$, lithium, and surface gravity. We find 218 confirmed or likely Taurus members, 160 confirmed or likely interlopers, and only 18 that still lack sufficient evidence to draw firm conclusions. A significant fraction of these stars (81/218=37%) are not included in the most recent canonical member lists. Intriguingly, there are few additional members in the immediate vicinity of the molecular clouds, preserving the IMFs that have been deemed anomalous in past work. Many of the likely Taurus members are distributed broadly across the search area. When combined with known disk hosts, our updated census reveals two regimes: a high-density population with a high disk fraction (indicative of youth) that broadly traces the molecular clouds, and a low-density population with low disk fraction (hence likely older) that most likely represents previous generations of star formation.
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