  The Gaia M-dwarf gap is a recently discovered feature in the colour-magnitude
diagram that shows a deficiency of low-mass and low-metallicity stars at the
lower end of the main sequence. We aim at performing theoretical stellar
modelling at low metallicities using a fine mass step and a fine time step,
looking specifically for the transition of models from partially to fully
convective, since the convective kissing instability that occurs at this
transition is believed to be the cause of the gap. Stellar evolution models
with metallicities of Z = 0.01, Z = 0.001 and Z = 0.0001 are performed using
MESA, with a mass step of 0.00025 M$_{\odot}$ and a time step of 50,000 years.
The small time step produced models that experience loops in their evolutionary
tracks in the Hertzsprung-Russell (HR) diagram. The fluctuations in effective
temperature and luminosity correspond to repeated events in which the bottom of
the convective envelope merges with the top of the convective core,
transporting $^3$He from the core to the surface. In addition to the episodes
of switching from partially to fully convective, several near-merger events
that produced low amplitude fluctuations were also found. Low-metallicity
models undergo the convective kissing instability for longer portions of their
lifetime and with higher fluctuation amplitudes than models with higher
metallicities. The small mass step used in the models revealed a discontinuity
in the luminosity-mass relation at all three metallicities.
