  Using spatially-resolved fossil record analysis on a large sample of 'red and
dead' elliptical galaxies (classical ellipticals, CLEs) from the MaNGA/SDSS-IV
DR15 survey, we reconstruct the archaeological evolution of their radial
gradients in mass-to-luminosity ratio ($M/L$), $g-r$ color, and specific star
formation (SF) rate. We also calculate other metrics that quantify the
inside-out SF quenching and external mass growth processes. The $M/L$
gradients, $\nabla\Upsilon_{\star}$, are approximately flat at high look-back
times ($t_{\rm lb}$), but then they become negative and steeper until an epoch,
when this trend reverses. These trends are shifted to later epochs the less
massive the galaxies are. Color gradients follow qualitatively similar trends.
We find that these trends are mainly driven by strong inside-out quenching,
without significant outer growth or structural changes overall. Our results
suggest a scenario where the main progenitors of local CLE galaxies evolved
quasi-passively after an early dissipative phase, but underwent radial
photometric changes due to the inside-out quenching that led to the systematic
decrease of $\nabla\Upsilon_{\star}$ and to an increase of the light-weighted
radius. The late reversing of $\nabla\Upsilon_{\star}$, $t_{\rm lb}\approx2-4$
Gyr, roughly coincides with the global quenching of the CLE galaxies. We have
pushed archaeological inferences to the limit, but thanks to the large number
of objects and an understanding of how the caveats and assumptions affect our
results, we conclude that they offer an average description of evolutionary
behaviors of CLE progenitors that is valid at least qualitatively.

Astrophysics of Galaxies