I was playing around with another set of graphics and my parallax backgrounds wouldn’t repeat more than once. After a while I think I worked it out. Godot seems to only have 2 copies of the sprite. This means that part of the screen can be left without the background graphic. In my case I had a 300 pixel wide background that I wanted to repeat across a 1920 width game window.
I think that this means the sprite needs to be at least a little larger than the game window width to ensure that a continuous scrolling background is possible.
Can someone double check this? I’m a total newb with Godot and I could easily be mistaken.