Anyone have any idea how much extra "positional" info one could extract out of the position of the sun + an accurate clock?

Granted, I know you couldn't quite get an exact 3d positional reading from just those. But the way I see it, these are complementary systems, and if possible, this extra "data-point" can add accuracy by further narrowing down possible actual locations. Sort of like overlapping 3d volumes (from different systems, with differing levels of accuracy), that allow you to triangulate your position. Each data-source incrementally removing "definitely-wrong" or "very-innacurate" data points from your end calculation.