  We show that on convex domains with sufficiently smooth boundary the limit
set of non-visible Kobayashi geodesics are contained in a complex face. In two
dimensions, this implies the existence of a complex tangential line segment of
non-Goldilocks points in the boundary. Conversely, we construct sequences of
non-visible almost-geodesics on convex domains whose boundary contains a
complex tangential line segment of non-Goldilocks points in a specific
direction.
