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The evolution of magnetism in late-type dwarfs remains murky, as we can only weakly predict levels of activity for M dwarfs of a given mass and age. We report results from our spectroscopic survey of M dwarfs in the Southern Continuous Viewing Zone (CVZ) of the Transiting Exoplanet Survey Satellite (TESS). As the TESS CVZs overlap with those of the James Webb Space Telescope, our targets constitute a legacy sample for studies of nearby M dwarfs. For 122 stars, we obtained at least one $R\approx 2000$ optical spectrum with which we measure chromospheric $\mathrm{H}α$ emission, a proxy for magnetic field strength. The fraction of active stars is consistent with what is expected for field M dwarfs; as in previous studies, we find that late-type M dwarfs remain active for longer than their early type counterparts. While the TESS light curves for $\approx$20% of our targets show modulations consistent with rotation, TESS systematics are not well enough understood for confident measurements of rotation periods ($P_{\mathrm{rot}}$) longer than half the length of an observing sector. We report periods for 12 stars for which we measure $P_{\mathrm{rot}} {\lower0.8ex\hbox{$\buildrel <\over\sim$}}$ 15 d or find confirmation for the TESS-derived $P_{\mathrm{rot}}$ in the literature. Our sample of 21 $P_{\mathrm{rot}}$, which includes periods from the literature, is consistent with our targets being spun-down field stars. Finally, we examine the $\mathrm{H}α$-to-bolometric luminosity distribution for our sample. Two stars are rotating fast enough to be magnetically saturated, but are not, hinting at the possibility that fast rotators may appear inactive in $\mathrm{H}α$.