Flat Earth or Globe, Observation from the Arctic Circle

From inside the arctic circle in the summer time when the sun is constantly visible day and night we should be able to make observations that would help to either prove or disprove the notion that the earth is a spinning globe orbiting a gigantic and very distant star.

 If the observer were able to rotate at the exact same speed as the earth but in the opposite direction as if mechanically attached to the stationary axis by a chain and set of identical sprockets and were facing the direction of the sun then what the observer should see on a spinning globe is the sun making an oval shaped path in the sky. To my knowledge this has not been attempted yet.

In the videos that I have seen of the midnight arctic sun the camera is actually tracking the sun through the sky which means that on a spinning globe the camera would not be rotating at the exact same speed as the rotation of the earth but would have to be speeding up and slowing down.

In order to track the path of the sun on a planet that is rotating as ours is said to be, the camera would have to be continuously rotating to the right (or clockwise as observed from above) in order to compensate for the rotation of the earth but rotating more quickly to the right during the daytime hours and more slowly to the right during the nighttime hours in order to compensate for the constant shifting from one side of the axis to the other.

The net result of this would be the appearance of the sun moving faster through the sky in the daytime since the camera would have to rotate more quickly to the right during the day and the appearance of the sun moving slower through the sky during the night time hours since the camera would have to rotate to the right more slowly at during the nighttime hours.

This does not appear to be the case.