  B[\,e\,] supergiants are a rare and unusual class of massive and luminous
stars, characterised by opaque circumstellar envelopes. GG Carinae is a binary
whose primary component is a B[\,e\,] supergiant and whose variability has
remained unsatisfactorily explained. Using photometric data from ASAS, OMC, and
ASAS-SN, and spectroscopic data from the Global Jet Watch and FEROS to study
visible emission lines, we focus on the variability of the system at its
$\sim$31-day orbital period and constrain the stellar parameters of the
primary. There is one photometric minimum per orbital period and, in the
emission line spectroscopy, we find a correlation between the amplitude of
radial velocity variations and the initial energy of the line species. The
spectral behaviour is consistent with the emission lines forming in the
primary's wind, with the variable amplitudes between line species being caused
by the less energetic lines forming at larger radii on average. By modelling
the atmosphere of the primary, we are able to model the radial velocity
variations of the wind lines in order to constrain the orbit of the binary. We
find that the binary is even more eccentric than previously believed
($e=0.5\pm0.03$). Using this orbital solution, the system is brightest at
periastron and dimmest at apastron, and the shape of the photometric variations
at the orbital period can be well described by the variable accretion by the
secondary of the primary's wind. We suggest that the evolutionary history of GG
Carinae may need to be reevaluated in a binary context.
