Benzophenone Ketyl color origin
TL;DR: The primary transition responsible for color is apparently the ${\pi{-}\pi}^*$ transition of the conjugated ketyl radical anion. This absorbs usually around the green to orange portions of the visible spectrum, leaving behind the purple-blue, and sometimes green color.

Original answer (background info):
According to Wikipedia/Benzophenone, the ketyl radical is formed by first, transition of the ketone from a singlet (double bond) to a triplet (diradical) state, and then abstraction of an electron from a donor to form the ketyl radical anion.
As I understand, only the radical anion is colorful. Both ref 1 and Wikipedia/Ketyl indicate that color disappears if the radical anion is allowed to oxidize (back to the ketone, which should be in equilibrium with the diradical). So my guess is, when an extra electron is added to the triplet state, this enables new electronic transitions that produce color.
These two sources also indicate both solvent and substituent effects: In the Wikipedia article, the solvent is toluene, and color is deep blue for benzophenone. In the paper, the solvent is isopropyl alcohol, and color is greenish-blue for benzophenone, and varies from blue to green depending on substituents. This also suggests that conjugation plays an effect, since the substituents can directly affect only the phenyls. But this, in turn, affects the energy levels of the double bond.

Edit:
A Google search for &quot;benzophenone ketyl spectrum&quot; (including the image search) gives several results of varying relevance, such as refs 2-4. In particular, from ref 2 (dealing with uranium ketyl radicals):

The electronic absorption spectrum of 2 in toluene features an intense absorption band ($\lambda_\text{max} = \pu{562 nm}$, $\epsilon = \pu{5680 M^{-1} cm^{-1}}$) in the visible region (Figure 8, top). This absorption gives rise to the ketyl complex’s distinctive and intense purple color and is assigned to the ${\pi{-}\pi}^*$ transition of a highly conjugated ketyl system. The transition energy of $\pu{562 nm}$ is blue-shifted from that of the sodium benzophenone ketyl radical, which exhibits the ${\pi{-}\pi}^*$ transition at $\pu{618 nm}$.

Ref 3 talks about $D_1 \leftarrow D_0$ and subsequent $D_n \leftarrow D_1$ transitions, and provides an energy level diagram. I assume $D_n$ refers to the doublet states that form upon abstraction of a hydrogen by (or addition of an electron to) the triplet diradical.
Finally, ref 4 adds:

Bzp is known to have a high ISC quantum yield following UV excitation, but until recently the mechanism of population of the lowest triplet excited state ($T_1$) after photoexciting to its $S_1$ (${nπ}^*$) state remained uncertain. ... These investigations indicate that the dominant pathway involves fast ISC from $S_1$ to $T_2$ (${\pi\pi}^*$) as an intermediate state, with the subsequent rate of population of the lowest vibrational levels of $T_1$ controlled by the time scale for dissipation of excess vibrational energy to the solvent bath after internal conversion (IC) from $T_2$.

(Bzp = benzophenone, ISC = intersystem crossing). It then proceeds to discuss these transitions in more detail.


J. Am. Chem. Soc. 1933, 55 (1), 391–395; doi:10.1021/ja01328a057
J. Am. Chem. Soc. 2008, 130 (20), 6567–6576; doi:10.1021/ja801007q
J. Phys. Chem. A 2004, 108 (40), 8147–8150; doi:10.1021/jp047058a
J. Am. Chem. Soc. 2019, 141 (38), 15222–15229; doi:10.1021/jacs.9b07047