The question was "Where would magnetism fit in this model?". Kaluza theory says: "It will fit!"

So an advice could be: first get Minkowski-Space and Einstein-Equations done, before including Electromagnetism.

I think, that a light cone should be only one causal knot (!)
(for a photon time stands still and everything is beyond event horizon, but it transports an interaction between generation point and absorption point).

Here is a classic paper from 1994 that might be of interest with regard to Kaluza-Klein theory. https://arxiv.org/abs/hep-th/9410046

That Kaluza-Klein theory feels very appealing. I am not an expert and I am not quite grasping many aspects of it, but if just by adding a fifth dimension the electromagnetism follows then it is a argument for electromagnetism not being rule specific.

There seem to be several possible compactifications on Kaluza-Klein. And since we are discussing a discrete model we should have more candidates. If we have an structure like the Cartesian product of three large cycles (the three spatial dimensions) and some graph G. For what kind of graphs G we would get the electromagnetism from Kaluza-Klein? I guess that G should have low diameter, so that that 'dimension' is not observable as a spacelike dimension.

Keep in mind, electromagnetism is a special case of a gauge theory. We are not currently trying to find electromagnetism itself, which will likely be rule-specific (although we will search for it in the future). We are now just trying to understand how gauge theories would work in our models in general.