This is the second paper in a series that considers first-order, gauge-invariant and covariant, gravitational perturbations to locally rotationally symmetric (LRS) class II vacuum spacetimes. Focusing on the 1+1+2 gravito-electromagnetic (GEM) formalism, the first paper used linear algebra techniques to derive four decoupled equations that govern four specific combinations of the GEM 2-tensor harmonic amplitudes. This paper completes the decoupling of the 1+1+2 GEM system by showing how to derive seven new decoupled quantities. Four of these arise when considering the GEM 2-vector harmonic amplitudes and it is found that decoupling is achieved by combining these with the (2/3-sheet) shear 2-tensor harmonic amplitudes. The remaining three arise from the 1+1+2 GEM scalars. Two of which concern the 2-gradient of the gravito-electric scalar that must also be combined with shear 2-tensor amplitudes, whereas the other involves the gravito-magnetic scalar only.