  This is the second in a series of papers which considers first-order
gauge-invariant and covariant gravitational perturbations to locally
rotationally symmetric (LRS) class II space-times. This paper shows how to
decouple a complex combination of the gravito-electromagnetic (GEM) 2-vectors
with the 2-tensors describing the shear of the 2/3-sheets. An arbitrary
harmonic expansion is then used along with an eigen-vector/value analysis of
the first-order GEM system, analogous to the first paper in this series. This
results in four real decoupled equations governing four real combinations of
the harmonic amplitudes of the GEM 2-vectors and the (2/3-sheet) shear
2-tensors. Finally, these are categorized into polar and axial perturbations.
