Half-mile programmable light chase possible?

Boffin1:
OK , this is not using an arduino, but a very much older, dirt cheap chip - the 555

Yes, that seems like the way to do it. Three wires, and cheap and readily available hardware at each node.

I wouldn't fancy building and connecting thousands of those by hand, though. Maybe you could find a cheap fab house willing to do a production run for you? If you use insulation displacement connectors it would speed up the wiring job, although it will still take an age. Then there's the question of mounts and enclosures and weather proofing. Simply putting down half a mile of cable is no small job, and presumably you'd want some means to remove individual units for repair without digging up the whole thing.