Ok, so the evidence seems to suggest that AppleScript is not an option. So we move to "plan C"... Image Searching.
What we need to do is plan out how to move the mouse to an image and click. What most people probably think is that we have to click directly inside the found image... but this is not true at all. For example, we could use the image search action to find the magnifying glass icon in the upper corner of the pop-up and click 200 pixels below it. This is why I wanted to see your whole window, because I'm looking for the most unique part of the window to search on. Part of the problem is that we can see the pop-up window is translucent, but that's not a fatal problem because the KM image search ability is very capable at covering approximate matches.
Before I go on, I'd like to point out that you may have better results if you turn your screen background to a solid black. That's because the translucency of the pop-up window won't show as much blue. However your blue is fairly dark and I don't think it should matter too much. But I mention this as a way to get you think about making the match more likely to work.
I can see different reasons for choosing different parts of the pop-up window as the search image. I'm not sure what you tried searching for, nor am I sure what you meant by "I had limited success." The "+" button has some good contrast, which I think should work, but if it doesn't work we have other options.
So my first action would be to locate the plus button by searching for an area that includes the plus button and some of the area around it. Here's what I would search for:
Notice that my search included the minus button and some dark area above the plus button. This helps with searches by eliminating false positives. Let me know if this works for you in terms of locating the plus button. If it works, we can then move on to the next buttons.
The subsequent steps will be easier if this step works, so try this first.
