  B[e] supergiants have unusual circumstellar environments which may include
thin, concentric rings displaying atomic line emission. GG Carinae is a B[e]
supergiant binary which exhibits such a geometry in its circumbinary
environment. We study atomic emission lines arising from GG Carinae's
circumbinary disc in FEROS spectra collected between 1998 and 2015. We find
that semi-forbidden Fe\,II] and permitted Ca\,II emission are formed in the
same thin circumbinary ring previously reported to have forbidden [O\,I] and
[Ca\,II] emission. We find that there are two circumbinary rings orbiting with
projected velocities of $84.6\pm1.0$\,km\,s$^{-1}$ and
$27.3\pm0.6$\,km\,s$^{-1}$. Deprojecting these velocities from the
line-of-sight, and using updated binary masses presented by
\cite{Porter2021GGPhotometry}, we find that the radii of the circumbinary rings
are $2.8^{+0.9}_{-1.1}$\,AU and $27^{+9}_{-10}$\,AU for the inner ring and
outer ring respectively. We find evidence of subtle dynamical change in the
inner circumbinary ring over the 17 years spanned by the data, manifesting in
variability in the ratio of the intensity of the blueshifted peak to the
redshifted peak of its emission lines and the central velocity becoming more
blueshifted. We perform smoothed-particle hydrodynamic simulations of the
system which suggest that these observed changes are consistent with pumping of
the eccentricity of a radially thin circumbinary ring by the inner binary. We
find a systemic velocity of the GG Carinae system of $-23.2 \pm
0.4$\,km\,s$^{-1}$.
