We consider the combined effects that overshooting and the 12C({\alpha},
{\gamma})16O reaction rate have on variable white dwarf stellar models. We find
that carbon-oxygen white dwarf models continue to yield pulsation signatures of
the current experimental 12C({\alpha}, {\gamma})16O reaction rate probability
distribution function when overshooting is included in the evolution. These
signatures hold because the resonating mantle region, encompassing
β\,0.2\,\Msun\ in a typical β\,0.6\,\Msun\ white dwarf model,
still undergoes radiative helium burning during the evolution to a white dwarf.
Our specific models show two potential low-order adiabatic g-modes, g2β and
g6β, that signalize the 12C({\alpha}, {\gamma})16O reaction rate probability
distribution function. Both g-mode signatures induce average relative period
shifts of ΞP/P=0.44% and ΞP/P=1.33% for g2β and g6β
respectively. We find that g6β is a trapped mode, and the g2β period
signature is inversely proportional to the 12C({\alpha}, {\gamma})16O reaction
rate. The g6β period signature generally separates the slower and faster
reaction rates, and has a maximum relative period shift of ΞP/P=3.45%. We conclude that low-order g-mode periods from carbon-oxygen white
dwarfs may still serve as viable probes for the 12C({\alpha}, {\gamma})16O
reaction rate probability distribution function when overshooting is included
in the evolution.Comment: 18 pages, 10 total figures, 2 online interactive figures, zenodo data
set link included. Accepted to the Astrophysical Journa