  Low-mass models of M-dwarfs that undergo the convective kissing instability
fluctuate in luminosity and temperature resulting in a gap in the main sequence
that is observed in the $Gaia$ data. During this instability, the models have
repeated periods of full convection where the material is mixed throughout the
model. Stellar evolution models are performed using MESA with varying amounts
of convective overshooting and semi-convection. We find that the amplitude and
intensity of the instability is reduced with increasing amounts of overshooting
but sustained when semi-convection is present. This is reflected in the loops
in the evolutionary tracks in the Hertzsprung-Russell diagram. The surface
abundances of $^1$H, $^3$He, $^4$He, $^{12}$C, $^{14}$N and $^{16}$O increase
or decrease over time due to the convective boundary, however the relative
abundance changes are very small and not likely observable. The mass and
magnitude values from the models are assigned to a synthetic population of
stars from the mass-magnitude relation to create colour-magnitude diagrams,
which reproduce the M-dwarf gap as a large indent into the blueward edge of the
main sequence (MS). This is featured in the luminosity function as a small peak
and dip. The width of the MS decreases over time along with the difference in
width between the MS at masses higher and lower than the instability. The
parallel offset and relative angle between the upper and lower parts of the MS
also change with time along with the mass-magnitude relation. Potential
age-dating methods for single stars and stellar populations are described.
