With another piece of shelf liner paper about the size of the ribbon logo, laminate that to the exposed sticky side of the ribbon logo sewn into the scarf.
Take a couple of layers of your diffusing material and place it up to cover the see-through part of the ribbon logo.
You can sandwich some loose fiberfill with a piece of thin white material.
Flip it over and with a close zigzag stitch, go around the outline of the logo. This will clean up and bind the edge of where you cut out the ribbon logo design.
I am using a bicycle flasher unit that has a belt clip attached.
I can make a reinforced slot for the bicycle flasher to clip in place.
You can of course take this further if you want to use an arduino to drive the LEDs or do some soft circuits with conductive thread in placing the LEDs. Change the lighting to match the color of the scarf, may need RGB LEDs.
I positioned the bicycle flasher to determine where I needed the hanger slot. I just sewed in a felt piece and essentially made a big buttonhole with several seams that boxed in the opening. I then cut between two seams to create the opening.