You can make a reasonable job of defining a pattern from the design, but the alignment is not good as it stands.
Drag a rectangular selection across the image while holding down the Shift key to force it to be square, and try and align it to the outside of a set of blocks.
Drag out some guides and let them snap to the selection like below.
Now Free Transform the selection to achieve corner to corner alignment with the guides.
Tip: Hold down the Ctrl (Cmd) key and drag the corner handles to align the blocks to the guides.
OK that, and drag out a selection and let it snap to the guides.
Go Image > Crop followed by Edit > Define Pattern
You can now fill an area with that pattern, and keep your fingers crossed that you did a decent job with the edge alignment
Looking at what I have just done, the corners are not too bad, but the irregular nature of the design means that it is not perfect in the central area of the outside edges. If you click on the screen shot below to expand it, you'll see what I mean. When I build something like this from scratch, I work with the grid turn on and scaled accordingly, and use the grid to achieve side to side, and top to bottom alignment. The central areas can deviate without spoiling the eventual pattern fill
I didnt really think about just tiling the scan itself because it wasnt the best scan to begin with. That might be an option though if I cant find a way to make it from scratch. I did do something in Illustrator that I thought was acceptable but apparently it wasnt. Ill use your idea as a last resort though, thanks!
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The actual filter used looks like Filter-Stylize-Tiles, run a few times with different settings.