My goal is to visualize somehow the curvature of time, as opposed to the curvature of space. I know that we generally talk about spacetime curvature altogether; however, the fact that spacetime has signature (+, +, +, -) indeed shows that time is a "special" component --> it is the only one which carries the minus sign. Hence, I expect that even geometrically the time curvature should be peculiar with respect to space curvature.
Now, if we focus only on $x$ spatial axis and time $t$, then we could depict the simplified-curved-spacetime as a 2D pseudo-Riemannian manifold (signature (+,-) ). Compare it to a 2D proper-Riemannian manifold as a sphere (signature (+,+) ).
Of course I know how to visualize a sphere; but is there a way to visualize a pseudo-Riemannian 2d manifold? Can I visualize the difference with respect to a proper-Riemannian 2d manifold (like the sphere)?