I am not particularly knowledgeable in this part of the Wolfram Model, but I had some ideas which may help define light-like, space-like and time-like events, while avoiding any imbedding (I suspect some of them may be already be present in Gorard's paper, but I haven't read all of it).
In special relativity, events inside the light cone can be reached by several light-like curves, while events on the boundary can be reached by only one light-like curve. The light-like events in WM could be defined in a similar way: two events A and B are light-like connected, if there exists only one unidirected causal chain connecting them (A->...->B or B->...->A) (two paths are considered equal, if they contain the same sequence of nodes). Similarly, two events are space-like connected, if there is no unidirected chain that would connect them; and two events are time-like connected, if there are more than one unidirected chain connecting them.
Do you think this would work?
