They seem 2 completely different systems and trying to translate the texture to (0.5, 0.5) in Blender doesn’t seem to work with any angle value (just tried).
That nodegroup is just for rotation, trying to translate or scale with that nodegroup is pointless, I thought it was obvious. Why did you even try that? You can always use the mapping node for translation and scaling.
The location value indicates the origin of the gradient where everything to the left is black and everything to the right is a gradient to white. 0-1 indicates the UV co-ordinates in this case. 1 (right) is full white and 0 (left) is black.
So x 0,y 0 is rotating the gradient from the bottom left of UV space. Sliding the values interactively in the rotation field will show this. So when you rotate 180 you have just made everything to the right black instead of everything to the left. Adding a value of 1 then simply moves the origin over to the farthest right of UV space. And then your black is trailing off to the next tile to the right instead of to the tile to the left.
Remember the input in vector is the UV map. So you are driving he gradient from the UV and UV space. And you are also trying to rotate from there. And I think - if I understand your problem - you want these two values separate. One value to indicate the origin of the gradient and another to indicate the rotation center.
So to have more control you could add a Vector Curve node between the Mapping node and the Gradient Texture node. This would allow you to rotate from .5.5 and tweak the curve to adjust the position of the gradient separately.
I should probably point out (for others reading this) that the easiest solution to achieve what I wanted is just rotating the UV quad in the UV Editor.
I knew that already, but I was trying to understand how the Mapping node works with textures.
The solution suggested by Richard (curve node) offers way more control over the gradient and it might be the best one for something more “advanced”.
I am going to mark the thread as solved now. Thanks everyone for posting and helping me.