Thanks, digitaldoc. I've updated the post with the video embedded.
ETA: The 25% of the time it's NOT flickering, black, or a solid color on that strip of screen, it works fine. I'm basically trying to assess whether this is a relatively easy fix, or if it's time for a new television. I've always been told that televisions are rarely worth the money spent fixing them, so I'm wary about taking this into a shop just yet.
Indeed, it does this whether I'm using cable, watching a blu-ray, streaming, etc, so does this despite the source or connection. Thanks for chiming in -- looks like it's time to go shopping.