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We detail the follow up and characterization of a transiting exo-Venus identified by TESS, GJ 3929b, (TOI-2013b) and its non-transiting companion planet, GJ 3929c (TOI-2013c). GJ 3929b is an Earth-sized exoplanet in its star's Venus-zone (P$_{b}$ = 2.616272 $\pm$ 0.000005 days; S$_{b}$ = 17.3$^{+0.8}_{-0.7}$ S$_{\oplus}$) orbiting a nearby M dwarf. GJ 3929c is most likely a non-transiting sub-Neptune. Using the new, ultra-precise NEID spectrometer on the WIYN 3.5 m Telescope at Kitt Peak National Observatory, we are able to modify the mass constraints of planet b reported in previous works and consequently improve the significance of the mass measurement to almost 4$σ$ confidence (M$_{b}$ = 1.75 $\pm$ 0.45 M$_{\oplus}$). We further adjust the orbital period of planet c from its alias at 14.30 $\pm$ 0.03 days to the likely true period of 15.04 $\pm$ 0.03 days, and adjust its minimum mass to m$\sin i$ = 5.71 $\pm$ 0.92 M$_{\oplus}$. Using the diffuser-assisted ARCTIC imager on the ARC 3.5 m telescope at Apache Point Observatory, in addition to publicly available TESS and LCOGT photometry, we are able to constrain the radius of planet b to R$_{p}$ = 1.09 $\pm$ 0.04 R$_{\oplus}$. GJ 3929b is a top candidate for transmission spectroscopy in its size regime (TSM = 14 $\pm$ 4), and future atmospheric studies of GJ 3929b stand to shed light on the nature of small planets orbiting M dwarfs.