  Although red clump stars function as reliable standard candles, their surface
characteristics (i.e. $T_\text{eff}$, $\log g$, and [Fe/H]) overlap with those
of red giant branch stars, which are not standard candles. Recent results have
revealed that spectral features containing carbon (e.g. CN molecular bands)
carry information correlating with the "gold-standard" asteroseismic
classifiers that distinguish red clump from red giant branch stars. However,
the underlying astrophysical processes driving the correlation between these
spectroscopic and asteroseismic quantities in red giants remain inadequately
explored. This study aims to enhance our understanding of this
"spectro-seismic" effect, by refining the list of key spectral features
predicting red giant evolutionary state. In addition, we conduct further
investigation into those key spectral features to probe the astrophysical
processes driving this connection. We employ the data-driven The Cannon
algorithm to analyse high-resolution ($R\sim80,000$) Veloce Rosso spectra from
the Anglo-Australian Telescope for 301 red giant stars (where asteroseismic
classifications from the TESS mission are known for 123 of the stars). The
results highlight molecular spectroscopic features, particularly those
containing carbon (e.g. CN), as the primary indicators of the evolutionary
states of red giant stars. Furthermore, by investigating CN isotopic pairs
(that is, $^{12}$C$^{14}$N and $^{13}$C$^{14}$N) we find suggestions of
statistically significant differences in the reduced equivalent widths of such
lines, suggesting that physical processes that change the surface abundances
and isotopic ratios in red giant stars, such as deep mixing, are the driving
forces of the "spectro-seismic" connection of red giants.
