  We determine the mass-ratio, eccentricity and binary inclination angles that
maximize the contribution of the higher-order waveform multipoles $(\ell, \,
|m|)= \{(2,\,2),\, (2,\,1),\, (3,\,3),\, (3,\,2), \, (3,\,1),\, (4,\,4),\,
(4,\,3),\, (4,\,2),\,(4,\,1)\}$ for the gravitational wave detection of
eccentric binary black hole mergers. We carry out this study using numerical
relativity waveforms that describe non-spinning black hole binaries with
mass-ratios $1\leq q \leq 10$, and orbital eccentricities as high as $e_0=0.18$
fifteen cycles before merger. For stellar-mass, asymmetric mass-ratio, binary
black hole mergers, and assuming LIGO's Zero Detuned High Power configuration,
we find that in regions of parameter space where black hole mergers modeled
with $\ell=|m|=2$ waveforms have vanishing signal-to-noise ratios, the
inclusion of $(\ell, \, |m|)$ modes enables the observation of these sources
with signal-to-noise ratios that range between 30\% to 45\% the signal-to-noise
ratio of optimally oriented binary black hole mergers modeled with $\ell=|m|=2$
numerical relativity waveforms. Having determined the parameter space where
$(\ell, \, |m|)$ modes are important for gravitational wave detection, we
construct waveform signals that describe these astrophysically motivate
scenarios, and demonstrate that these topologically complex signals can be
detected and characterized in real LIGO noise with deep learning algorithms.
