I was recently preparing the benzophenone ketyl radical by reacting it with sodium in toluene. Although this compound is really well known and it seems somewhat obvious and accepted in literature that the radical causes a color I am still unable to find anything on the actual transition. There are some luminescence experiments but at least to my research there doesn't seem to be a good explanation on the actual color.
My suggestion would be that perhaps occupying the former LUMO of the benzophenone to generate a SOMO causes the orbital to shift in energy. I always confuse when something is stabilized or destabilized but since it seems to be in interaction with the two benzene rings I'd suggest that by occupying the orbital you can also lower it in energy a bit and thus promote the excitation of a former HOMO electron into the singly occupied SOMO with visible light.
According to what I found there are various mechanisms depending on the environment around the radical orbital how it can stabilize itself and thus lower the gap between the two orbitals (former HOMO and new SOMO).