  AM CVn-type systems are ultra-compact, hydrogen-deficient accreting binaries
with degenerate or semi-degenerate donors. The evolutionary history of these
systems can be explored by constraining the properties of their donor stars. We
present high-speed photometry of Gaia14aae, an AM CVn with a binary period of
49.7 minutes and the first AM CVn in which the central white dwarf is fully
eclipsed by the donor star. Modelling of the lightcurves of this system allows
for the most precise measurement to date of the donor mass of an AM CVn, and
relies only on geometric and well-tested physical assumptions. We find a mass
ratio $q = M_2/M_1 = 0.0287 \pm 0.0020$ and masses $M_1 = 0.87 \pm 0.02
M_\odot$ and $M_2 = 0.0250 \pm 0.0013 M_\odot$. We compare these properties to
the three proposed channels for AM CVn formation. Our measured donor mass and
radius do not fit with the contraction that is predicted for AM CVn donors
descended from white dwarfs or helium stars at long orbital periods. The donor
properties we measure fall in a region of parameter space in which systems
evolved from hydrogen-dominated cataclysmic variables are expected, but such
systems should show spectroscopic hydrogen, which is not seen in Gaia14aae. The
evolutionary history of this system is therefore not clear. We consider a
helium-burning star or an evolved cataclysmic variable to be the most likely
progenitors, but both models require additional processes and/or fine-tuning to
fit the data. Additionally, we calculate an updated ephemeris which corrects
for an anomalous time measurement in the previously published ephemeris.
