  Background: The structure of the Hoyle state, a highly $\alpha$-clustered
state at 7.65 MeV in $^{12}\mathrm{C}$, has long been the subject of debate.
Understanding if the system comprises of three weakly-interacting
$\alpha$-particles in the 0s orbital, known as an $\alpha$-condensate state, is
possible by studying the decay branches of the Hoyle state. Purpose: The direct
decay of the Hoyle state into three $\alpha$-particles, rather than through the
$^{8}\mathrm{Be}$ ground state, can be identified by studying the energy
partition of the 3 $\alpha$-particles arising from the decay. This paper
provides details on the break-up mechanism of the Hoyle stating using a new
experimental technique. Method: By using beta-delayed charged-particle
spectroscopy of $^{12}\mathrm{N}$ using the TexAT (Texas Active Target) TPC, a
high-sensitivity measurement of the direct 3 $\alpha$ decay ratio can be
performed without contributions from pile-up events. Results: A Bayesian
approach to understanding the contribution of the direct components via a
likelihood function shows that the direct component is $<0.043\%$ at the 95\%
confidence level (C.L.). This value is in agreement with several other studies
and here we can demonstrate that a small non-sequential component with a decay
fraction of about $10^{-4}$ is most likely. Conclusion: The measurement of the
non-sequential component of the Hoyle state decay is performed in an almost
medium-free reaction for the first time. The derived upper-limit is in
agreement with previous studies and demonstrates sensitivity to the absolute
branching ratio. Further experimental studies would need to be combined with
robust microscopic theoretical understanding of the decay dynamics to provide
additional insight into the idea of the Hoyle state as an $\alpha$-condensate.
