You may be right that those squiggles are created in AE, but to me they look very much like the beginning/end of a reel of developed film. What I think it is is notes written on the film negative in black marker which becomes white when the film is printed. He probably took a digitized version of this and used the “add” blend mode. If you wanted to create your own you could probably just write a sentence with black marker on a white piece of paper, scan it, apply a negative effect to the colors, and overlay it on your video. You would also want to animate it moving up rapidly, maybe at 12fps and a lot of motion blur. Maybe add a wiggle expression as well to make it jittery.
P.S. I’ll have to side with Dave and iancorey- the vignette looks cheesy.