The thread must travel between components to connect them, while avoiding other paths of conductive thread in the circuit. The thread acts like uninsulated wire or traces on a circuit board, but this circuit board is made out of fabric!
The most straightforward connection is a running stitch. You can also learn many more hand embroidery stitches which can have decorative or functional appeal in your project.
As you stitch along, pause periodically to whip-stitch a chainable pixel's ground pad (-).
Turning 180 degrees
Now that all the pixels are anchored by one pad, clean up any stray threads on the back.