  We report a systematic study of all known methyl carbon chains toward TMC-1
using the second data release of the GOTHAM survey, as well as a search for
larger species. Using Markov-Chain Monte Carlo simulations and spectral line
stacking of over 30 rotational transitions, we report statistically significant
emission from methylcyanotriacetylene (CH$_3$C$_7$N) at a confidence level of
4.6$\sigma$, and use it to derive a column density of ${\sim}$10$^{11}$
cm$^{-2}$. We also searched for the related species, methyltetraacetylene
(CH$_3$C$_8$H), and place upper limits on the column density of this molecule.
By carrying out the above statistical analyses for all other previously
detected methyl-terminated carbon chains that have emission lines in our
survey, we assess the abundances, excitation conditions, and formation
chemistry of methylpolyynes (CH3C$_{2n}$H) and methylcyanopolyynes
(CH3C$_{2n-1}$N) in TMC-1, and compare those with predictions from a chemical
model. Based on our observed trends in column density and relative populations
of the A and E nuclear spin isomers, we find that the methylpolyynes and
methylcyanopolyynes families exhibit stark differences from one another,
pointing to separate interstellar formation pathways, which is confirmed
through gas-grain chemical modeling with nautilus.
