We have the Gurdon Light here in southern Arkansas. It is quite regular as well. Since the lights are associated with an active railroad track, I guess that is involves some light source reflecting off the shiny rail.

Eerie? Yes.

Supernatural? Most probably not.

If only the rail line would let me spray a few miles of track flat black...

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In the progress of this discussion I shall endeavor to give a satisfactory answer to all the objections which shall have made their appearance, that may seem to have any claim to your attention.

Alexander Hamilton, Federalist No. 1