There is already a short entry for Indexed Image/Color.
Personally, I never gave Index Painting much explicit thought because in all pixel art tools I've used (starting with PaintMagic on the C64 and DPaintIII on the Amiga500), "Index Painting" (though it was not called that back then I think, it didn't seem to have a name then) was just the default or only mode the tools and hardware(like the C64) could even handle, so to me, that was always the natural way to go/think about pixel art.
With non-indexed modes around today however, "Index Painting"(what making Pixel Art really already always was imo) should indeed be mentioned separately, but I suggest in more than just one additional entry, broken down into more specific terms:
Index Painting (broad generalization goes into that with links to Dan's articles)
Pallete Swap (full and partial swaps, with examples like faction colors in strategy games or a number of "identical" grayscales for different elements like clothes for individual partial swaps per element)
Color Cycling (a special case of a number of "Pallete Effects")
Palette Structure (logical mapping between palette indices and objects those indices will be used for (skin colors, shoe colors, ... closely related to preparing something for effects like Color Cycling and partial or full Palette Swaps)
Pallete Effects (umbrella term for things like Color Cycling, Palette Swaps, Palette Fading)
The fact, that using automated tools ( "dirty" as they're often called) which cause mutations of affected pixels by color without caring about indices, are mostly unsuitable if Palette Structure is important for programmatic effects seems obvious but maybe it should be mentioned in an entry about "'Dirty' Tools" without condemning them as forbidden though, just to point out that their usage can require manual cleanup and making sure each pixel refers to the correct palette index after applying them (seems though that this might be better covered in a tutorial about Palette Structure as it's pretty longwinding for a brief description which aims to be free of judgement).
Added example and fleshed out description to the existing Pillow Shading entry: