  Galaxy pairs with separations of only a few kpc represent important stages in
the merger-driven growth of supermassive black holes (SMBHs). However, such
mergers are difficult to identify observationally due to the correspondingly
small angular scales. In Paper I we presented a method of finding candidate
kpc-scale galaxy mergers that is leveraged on the selection of X-ray sources
spatially offset from the centers of host galaxies. In this paper we analyze
new Hubble Space Telescope (HST) WFC3 imaging for six of these sources to
search for signatures of galaxy mergers. The HST imaging reveals that four of
the six systems are on-going galaxy mergers with separations of 1.2-6.6 kpc
(offset AGN). The nature of the remaining two spatially offset X-ray sources is
ambiguous and may be associated with super-Eddington accretion in X-ray
binaries. The ability of this sample to probe small galaxy separations and
minor mergers makes it uniquely suited for testing the role of galaxy mergers
for AGN triggering. We find that galaxy mergers with only one AGN are
predominantly minor mergers with mass ratios similar to the overall population
of galaxy mergers. By comparison, galaxy mergers with two AGN are biased toward
major mergers and larger nuclear gas masses. Finally, we find that the level of
SMBH accretion increases toward smaller mass ratios (major mergers). This
result suggests the mass ratio effects not only the frequency of AGN triggering
but also the rate of SMBH growth in mergers.
