If I plot a 'time elapsed' versus 'distance traveled' graph of a photon travelling in a vacuum (time on the vertical axis and distance on the horizontal) and then take the volume of revolution about the time axis, will it somehow correspond to what we call a light cone?
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Your intuition is right, with a few caveats:
Technically, you should be talking about the surface of revolution, not the volume of revolution. A light ray can't travel between an event $A$ and some other event $B$ that lies inside the cone $ds^2 = 0$.
Spacetime is 4-D, and in higher dimensions, one can't talk about rotations "about an axis"; instead, one has to talk about rotations "within a plane". Of course, one has to suppress one of the spatial dimensions to be able to draw this cone, so this point is a bit academic; but it's still worth remembering that the light-cone is really a 3-D surface in a 4-D space.
Michael Seifert
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It is possible use calculus with extra dimensions to talk about rotations within a plane? – Feb 17 '18 at 06:34
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@Coder511: I'm not quite sure what you're asking. But if you want to learn more about rotations in higher dimensions, there's a pretty good overview at this question: Why are the generators of rotation in the 4-dimensional Euclidean space correspond to rotations in a plane? – Michael Seifert Feb 17 '18 at 14:43