'cleese, a good question and some fascinating replies. I've never thought of harmonies in terms of visualization, but as something I've had to struggle to learn. My partner has been singing at camps most of her early years and seems to find harmonies effortlessly, and how I envy that...
M Ted, I find harmonies in a similar way to you, by listening to the notes in a guitar chord and following the chord changes. Practice also improves the ear and one's ability to pick out harmonies.
I also have a wonderful resource, our song circle, where there are several who can find harmonies easily. I often sit next to one of them and try to sing along with them, as long as they don't accuse me of 'stealing their notes' *BG*... I've trained my ear that way.
Wyo, it's too bad you don't have a group to sing with, but you do have a practice space (your car) where you can try out different things along with tapes you are playing. Just keep your windows closed when you're in heavy city traffic and you won't get too many strange looks ..*grin* I recall a time when I was practicing harmonica, pulled up to a stop light, and was surprised by applause coming from the car next to me...

good thread.. cheers... Davey