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I initially thought this was a fox squirrel, but thought it was weird that it was going into a rock crevice on the side of the river. Inat suggested rock squirrel, so I decided to roll with it but I am not sure?

Plants and critters from Weymouth Woods, Moore County, NC (USA).
Fox Squirrel - Sciurus niger (melanistic), subspecies:
Southern Fox Squirrel - Sciurus niger niger
I have seen both dark phase and "fox-colored" squirrels at Weymouth Woods. Eastern Gray Squirrels also occur. This squirrel was gnawing avidly on the upper surface of the branch it was perched on (shown in one frame).

This is, I think, a fox squirrel and not a melanistic Eastern Gray Squirrel (Sciurus carolinensis). I was not close enough to judge the size in any way. Looking at images on the Internet, Fox Squirrels seem to have a more robust, less-tapered "snout" than Eastern Gray Squirrels. That matches the images here, to my eye. Other features I notice:

• Toes of this squirrel are quite robust (and more hairy?) compared to what I have seen in gray squirrels. Toe pads are quite prominent. (That would make sense for a Fox Squirrel, as they are more terrestrial than Gray Squirrels.)
• Ears appear to be shorter and more rounded than in Eastern Gray.
• Pelage coarse and shaggy.

Some of the putative distinctive features noted above are marked in one detail image. Most references just mention the size and pelage to differentiate from Eastern Gray Squirrel. One historical reference has helpful notes on other characters:
"A large, arboreal Squirrel of rather variable color pattern - much larger and heavier in build than the Eastern Gray Squirrels; pelage coarse and harsh; hands and feet large, soles naked; nose and ears always white."

• Anthony, Field Book of North American Mammals, 1928, p. 275 (BHL link)