  We develop a photometric search method for identifying smouldering galaxies
at $5< z < 8$, which are defined to have weak emission lines and thus generally
have low specific star formation rates and may even be in a state of
(temporary) quiescence. The deep NIRCam imaging (${\sim}29.5$ AB mag,
5$\sigma$) from the JADES second data release is essential for finding these
systems, as they are faint, relatively quiescent dwarf galaxies ($M_* \sim
10^{8}$-$10^9$ $\mathrm{M}_\odot)$ in the Epoch of Reionisation (EoR).
Moreover, medium-band imaging is key, enabling a clear identification of the
lack of emission lines in these galaxies, thus betraying their dormant flame.
Owing to the young age of the Universe, combined with the likely bursty star
formation in these first dwarf galaxies, conventional colour-selection methods
like the UVJ diagram likely miss a large fraction of the quiescent population
in the EoR. Indeed, we find that smouldering galaxies constitute a considerable
fraction (0.10-0.35) of the EoR dwarf galaxy population ($M_* \sim
10^{8}$-$10^{9}$ $\mathrm{M}_\odot$). As predicted by simulations, these first
dwarf galaxies are fragile, the star formation in their shallow potential wells
easily snuffed out by feedback-driven winds triggered by secular or
merger-driven starbursts, with the smouldering fraction increasing with
decreasing stellar mass. Finally, we provide observational constraints on the
smouldering galaxy comoving number density (${\sim}10^{-4}$-$10^{-5}$
dex$^{-1}$ Mpc$^{-3}$), which, although hampered by incompleteness, should aid
in our understanding of the primordial baryon cycle, as current simulations
greatly disagree on whether these systems are rare (${\sim}1\%$) or common
(${\sim}50\%$) in the EoR.
