Elliptical galaxies moving through the intra-cluster medium ( ICM ) are progressively stripped of their gaseous atmospheres . X-ray observations reveal the structure of galactic tails , wakes , and the interface between the galactic gas and the ICM . This fine-structure depends on dynamic conditions ( galaxy potential , initial gas contents , orbit in the host cluster ) , orbital stage ( early infall , pre-/post-pericenter passage ) , as well as on the still ill-constrained ICM plasma properties ( thermal conductivity , viscosity , magnetic field structure ) . Paper I describes flow patterns and stages of inviscid gas stripping . Here we study the effect of a Spitzer-like temperature dependent viscosity corresponding to Reynolds numbers , Re , of 50 to 5000 with respect to the ICM flow around the remnant atmosphere . Global flow patterns are independent of viscosity in this Reynolds number range . Viscosity influences two aspects : In inviscid stripping , Kelvin-Helmholtz instabilities ( KHIs ) at the sides of the remnant atmosphere lead to observable horns or wings . Increasing viscosity suppresses KHIs of increasing length scale , and thus observable horns and wings . Furthermore , in inviscid stripping , stripped galactic gas can mix with the ambient ICM in the galaxy ’ s wake . This mixing is suppressed increasingly with increasing viscosity , such that viscously stripped galaxies have long X-ray bright , cool wakes . We provide mock X-ray images for different stripping stages and conditions . While these qualitative results are generic , we tailor our simulations to the Virgo galaxy M89 ( NGC 4552 ) , where \textrm { Re } \approx 50 corresponds to a viscosity of 10 % of the Spitzer level . Paper III compares new deep Chandra and archival XMM-Newton data to our simulations .