Even if the stands are far away, even light years away, you pan through 360° every year. The fact that the background is far away means that it moves even quick

Even if the stands are far away, even light years away, you pan through 360° every year. The fact that the background is far away means that it moves even quicker relative to a nearby object in a rotational frame. If you spin around in a circle, hold your hand out and look at it, it will be moving very quickly against a distant background, like the horizon. My point is that the distance to the background helps detection, not hurts it. If the background was nearby and co-rotating around the Sun, detection would be a near impossible.