We present the $H$-band wavelength region of thirty post-maximum light near-infrared (NIR) spectra of fourteen transitional and sub-luminous type Ia supernovae (SNe Ia), extending from $+$5d to +20d relative to the epoch of $B$-band maximum. We introduce a new observable, the blue-edge velocity, $v_{edge}$, of the prominent Fe/Co/Ni-peak $H$-band emission feature which is quantitatively measured. The $v_{edge}$ parameter is found to slowly decrease over sub-type ranging from around $-$13,000km/s for transitional SNe~Ia, down to $-$5,000km/s for the sub-luminous SNe Ia. Furthermore, inspection of the +10$pm$3d spectra indicates that $v_{edge}$ is correlated with the color-stretch parameter, s$_{BV}$, and hence with peak luminosity. These results follow the previous findings that brighter SNe Ia tend to have $^{56}$Ni located at higher velocities as compared to sub-luminous objects. As $v_{edge}$ is a model-independent parameter, we propose it can be used in combination with traditional observational diagnostics to provide a new avenue to robustly distinguish between leading SNe Ia explosion models.
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