I do wonder if the simple sine oscillation is a tumbling satellite. If so, it being non-uniform in shape would catch sunlight in a repeating pattern. An example, consider a satellite with solar panels off each side. If it is spinning as it travels, then one side solar panel will catch the light and then the other.

The other thing I thought about is it could still be a mount issue. The stars in the attached image seem to be oblong in the same direction as the peaks of the sine wave. If the satellite travel was perpendicular to the error in the mount, it would show up the most vs the lower, fainter trail in the right corner, the fainter trail runs more parallel to the potential mount error. Parallel to the error would greatly reduce the magnitude of the error appearing in the trail as a much larger component of the oscillation is along the trail instead of perpendicular to it.

It seems too linear and uniform in pattern to be a firework I think.

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