Infrared excesses around white dwarf stars indicate the presence of various astrophysical objects of interest, including companions and debris disks. In this second paper of a series, we present follow-up observations of infrared excess candidates from Gaia and unWISE discussed in the first paper, Paper I. We report space-based infrared photometry at 3.6 and 4.5 micron for 174 white dwarfs from the Spitzer Space Telescope and ground-based near-infrared J, H, and K photometry of 235 white dwarfs from Gemini Observatory with significant overlap between Spitzer and Gemini observations. These data are used to confirm or rule out the observed unWISE infrared excess. From the unWISE-selected candidate sample, the most promising infrared excess sample comes from both color and flux excess, which has a Spitzer confirmation rate of 95%. We also discuss a method to distinguish infrared excess caused by stellar or sub-stellar companions from potential dust disks. In total, we confirm the infrared excess around 62 white dwarfs, 10 of which are likely to be stellar companions. The remaining 52 bright white dwarfs with infrared excess beyond two microns has the potential to double the known sample of white dwarfs with dusty exoplanetary debris disks. Follow-up high-resolution spectroscopic studies of a fraction of confirmed excess white dwarfs in this sample have discovered emission from gaseous dust disks. Additional investigations will be able to expand the parameter space from which dust disks around white dwarfs are found.