In this second of a two-paper series, we present a detailed analysis of three Hubble Space Telescope observations taken ∼2–4 yr post-discovery, examining the evolution of a UV-bright underlying source at the precise position of AT 2018cow. While observations at ∼2–3 yr post-discovery revealed an exceptionally blue (L
ν
∝ ν
1.99) underlying source with relatively stable optical brightness, fading in the near-UV was observed at year 4, indicating flattening in the spectrum (to L
ν
∝ ν
1.64). The resulting spectral energy distributions can be described by an extremely hot but small blackbody, and the fading may be intrinsic (cooling) or extrinsic (increased absorption). Considering possible scenarios and explanations, we disfavor significant contributions from stellar sources and dust formation, based on the observed color and brightness. By comparing the expected power and the observed luminosity, we rule out interaction with known radio-producing circumstellar material (CSM) as well as magnetar spin down with B ∼ 1015 G as possible power sources, though we cannot rule out the possible existence of a denser CSM component (e.g., a previously ejected hydrogen envelope) or a magnetar with B ≲ 1014 G. Finally, we find that a highly inclined precessing accretion disk can reasonably explain the color, brightness, and evolution of the underlying source. However, a major uncertainty in this scenario is the mass of the central black hole (BH), as both stellar-mass and intermediate-mass BHs face notable challenges that cannot be explained by our simple disk model, and further observations and theoretical works are needed to fully constrain the nature of this underlying source.