I have been watching period videos of engines traveling and on some of them the head light, is swiveling in a circle. as others stay in situ. why is this back and forth circle method used?. just curious.

The moving light isn't a headlight, it's a device with a similar intention to modern flashing ditch lights: to draw attention to the oncoming train. There were two major manufacturers, Mars and Gyralight. Both employed a mechanism that moved the light inside a housing in various set patterns so the light would appear to "flash" from any one viewpoint. They would be used in addition to a headlight, although you may be seeing video from a time before headlights were mandated to be used during daylight hours.