You have a very thin cylinder. Ellipsoid
seems to perform better if you are trying to emulate a disk.
cyl = Cylinder[{{(-0.1 + 10.128)/2, (13 + 1.3)/2,
0}, {(-0.1 + 10.128)/2, (13 + 1.3)/2, 0.001}}, 3.2];
centroid = RegionCentroid@cyl;
bnds = First@Differences@Transpose@RegionBounds@cyl;
ell = Ellipsoid[centroid, bnds];
Manipulate[
Graphics3D[{Specularity[White, 5], Style[ell, c]},
Lighting -> {{"Spot",
Red, {centroid + {0, 0, 3}, centroid}, θ}},
ImageSize -> Small], {{θ, π/2.5}, π/40, π/2}, {c,
White, ColorSlider}]

The following shows how the image changes at discrete surface colors with constant lighting.
Grid[{Graphics3D[{Style[ell, #]},
Lighting -> {{"Spot", Red, {centroid + {0, 0, 3}, centroid},
Pi/2.5}}] & /@ {White, Yellow, LightBlue, Blue}}]

The following shows how the image changes with underlying surface color under a White, Red, Green, and Blue spotlight.
mean = First@Mean@Transpose@RegionBounds@cyl;
tt = TranslationTransform /@ (DeleteCases[
Tuples[{0, #}, 3], {_, _, #}] &@bnds[[1]]*2.5);
ctt = Transpose[{{"White", "Red", "Blue", "Green"}, tt}];
Manipulate[
Graphics3D[{Specularity[White, 5],
Flatten@({Lighting -> {{"Spot",
ToExpression@#[[1]], #[[2]] /@ {centroid + {0, 0, 3},
centroid}, s}},
GeometricTransformation[
Style[{ell, Text[#[[1]], {mean, bnds[[1]]*2.3, 0}]}, c], #[[
2]]]} & /@ ctt)},
ViewPoint -> Top], {{s, Pi/5, "Spotlight Angle"}, Pi/20,
Pi/2.5}, {{c, Yellow, "Underlying Object Color"}, ColorSlider},
ControlPlacement -> Top]
