You are putting the tool in wrong. The blade part(curved) should face in towards the center of the CC unit. The straight edge should be facing to the outside of the unit.
Yes, you're absolutely right! I figured I could be putting it in the wrong way, so I tried it both ways before I created this thread, and it made no difference; it still wouldn't engage.
What I ended up doing after creating this thread was removing that white facing you saw in the video to expose virtually the whole mechanism in question and have a clear view of what was happening when I inserted the tool into the tool slot (the correct way). I saw that all that was happening was that the tip of the tool was just pushing against the flat metal of the mechanism with no engagement and little movement of the mechanism itself. At that point, I just gave up on using the tool in the conventional way and removed it from the tool slot and went above the slot into the big open space where that white facing was and used the tip of the tool to hook an upper part of the mechanism and pull it in medially (toward the center of the head unit) and was able to get it released! (Please see the pictures at the bottom of this post.)
In the end, despite my video demonstration of my effort putting the tool in the wrong way, it seems that what I was dealing with was a defective mechanism on the right side, as it wouldn't work even when I inserted the tool in the correct way and even after I was able to remove the head unit and try that tool and the other tool in that slot to see again if it would work.
It was frustrating, but at least now I know how to remove these factory head units when these mechanisms don't work. I was afraid I was going to have to remove the "wood" paneling, which is way above my current paygrade!
Thanks for your feedback, guys!