The observations of Gamma Draconis are a bit hard to visualize so here's a more detailed explanation and description.
First imagine that you are looking at a star whose position is in the plane of the Earth's orbit. The line in the sky that these points is called the 'ecliptic'. It is also the apparent path of the Sun across the sky.
What should happen to the position of a star that is one this line? Take a look at Fig.1. The top of the image shows the Sun as a yellow dot and the star being observed as a white dot. The earth is a blue ball with a VERY large telescope pointing in the average direction of the star The bottom half of the picture shows what you would see looking through this telescope.
Over an entire year the star would appear to move back and forth in a straight line, along the ecliptic.
Now imagine that the star is perpendicular to the plane of the Earth's orbit. There are two such points and they are called the 'ecliptic poles'. Parallax would make a star at one of these poles would appear to go in a circle around the pole. See Fig.2.
For a star in between these locations the apparent path would be an ellipse with the long diameter parallel to the ecliptic. The largest shift will occur when the angle between the Sun/Earth line and the Eart/Star line is 90°
But this isn't what was seen. The observed shift was 10 times bigger than estimated and the minimum occured when the maximum was predicted.
Even worse, when the observations were done on other stars the size of the shift depended only on the position of the star in the sky.
So what was going on? Bradley figured it out.