I agree with your interpretation, but there are those charts which show varying degrees of clarity of mental images (using an apple), I don't understand how to square that with just invoking the sense instead of actually seeing it.
Fro me it feels that imagining things uses completely different brain part, because for me it does not feel or look like stuff in my dreams or what eyes can see, imagining things feel different,the scenes feel to me unclear, disappear fast , I do not have the ability to lock the image or rewind like in a video. Remembering a recent scene has a lot more details and colors then some old memory.
For geometry stuff is the same, I can't say I see it but somehow I have an animation my head on how I can transform the geometric stuff, but it is not vivid and it is not like a clear video, feels like is a different part of the brain that does this not the optic part.
There are very few occasions when I wake up and really have the memory of an image. But this fades so fast that I’m not able to really describe the image. I retain the memory of having a picture in my head. And it’s boring most of the time, because it happens in the middle of a dream and it’s basically just the last frame paused.
This analogy may be less communicative than you think, as for me, reading a book is like watching a movie - I don’t see the words on the page, I see what’s happening in the book.
For example, I was reading some Pratchett and noticed that I had no idea how the protagonist ended up on a cliff (?). And then realized that I had automatically skipped the paragraph that talked about the cliff ascent, because it was “just a scenery description” and therefore useless.
I also remember having a long argument with my ex-girlfriend about the style of journalism where articles start like “I entered a small, dimly-lit room and Mr Brown, age 53, stood up from his massive oak desk and [blah blah blah]”. Like, this is all just fluff, I want to know what Mr Brown says and thinks and that’s all. I didn’t realize people might actually imagine the scene and enjoy it.
Going back to books — I think I care about how the book sounds more than I care about the plot or the vibe. I loved Lolita solely because the narrator was constantly playing with words, for example.
But I cannot hold an image in my head. With concentration I can will an image into existence, but it does not hold still for even an instant. A shapeless tangle will interpolate into an apple and then back to a tangle.
But recently I realized I can visualize color, which was interesting.
And my audio/music recall is excellent.