My current layer order and an explanation of it is as follows:

The bone I have selected is what I named "blink", and the smart bone is named "blink" as well.
Within my character's layers, there is the selected "eyes bone group", which is a bone and contains all the individual bones that allow me to position my character's pupils and so on (I followed Poptoogi's general example), and is also where "blink" is located. That layer is contained within the blue-highlighted “eyes” group, which is a basic group folder that allows me to (if needed) move the actual eye bone layer around. Above that is the head folder, where the eyes, mouth switch layer, and other face/head features are.
The head is NOT bound to the main skeleton of the character rig – the individual components (both folders and individual/independent vector layers like her hair) are.
Now, as for what the error I’m having looks like, when I go into the smart bone action I created, the bone that’s currently cyan (“blink”) will be red until I click, at which point it goes to cyan and I instead start moving around the bone that’s selected in the screenshot below (which “blink” is not bound to).

I also realized, just before doing one final check before making this post, that when I hovered around in the space to the right of the eyes, there were little circles for manipulating something (presumably the eye bones). I don't know what caused that or what that even means, or if/how that's related to this.

What am I doing wrong here? Is it something that the bake script I was sent caused, or user error on my part?