  We analyze accretion-rate time series for equal-mass binaries in co-planar
gaseous disks spanning a continuous range of orbital eccentricities up to 0.8,
for both prograde and retrograde systems. The dominant variability timescales
match that of previous investigations; the binary orbital period is dominant
for prograde binaries with $e \gtrsim 0.1$, with a 5 times longer "lump" period
taking over for $e\lesssim 0.1$. This lump period fades and drops from 5 times
to 4.5 times the binary period as $e$ approaches 0.1, where it vanishes. For
retrograde orbits, the binary orbital period dominates at $e \lesssim 0.55$ and
is accompanied by a 2 times longer-timescale periodicity at higher
eccentricities. The shape of the accretion-rate time series varies with binary
eccentricity. For prograde systems, the orientation of an eccentric disk causes
periodic trading of accretion between the binary components in a ratio that we
report as a function of binary eccentricity. We present a publicly available
tool, binlite, that can rapidly ($\lesssim 0.01$~sec) generate templates for
the accretion-rate time series, onto either binary component, for choice of
binary eccentricity below 0.8. As an example use-case, we build lightcurve
models where the accretion rate through the circumbinary disk and onto each
binary component sets contributions to the emitted specific flux. We combine
these rest-frame, accretion-variability lightcurves with observer-dependent
Doppler boosting and binary self-lensing. This allows a flexible approach to
generating lightcurves over a wide range of binary and observer parameter
space. We envision binlite as the access point to a living database that will
be updated with state-of-the-art hydrodynamical calculations as they advance.
