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I've never seen any image of any kind in my mind, nor have I experienced any other imagined sense. Visual thinking is merely activity within a region of the brain associated with a visual experience. If you were to shoot a charged particle through your occipital lobe, you may experience it as a flash of light. Those with aphantasia process thought in a different region of the brain that is not associated with the experience of visualization.
Where that thought takes place will determine the structure and connections within the neural network that processes that information. Most complex neural networks can solve any basic problem, but some structures are more efficient, more accurate, or faster than others. When thought occurs in an atypical structure it can give rise to deficits or strengths. Synesthesia is a common example, but there are also examples of people with "human calculator" like abilities and more.
When you say visual thinking, visualization is merely an experience and is not necessary to solve multidimensional problems. It is however a very fast and efficient method to do so. Studies which have compared the problem solving abilities of those with aphanatasia and visual thinkers found that those who relied on visualization were faster, but less accurate problem solvers. I'm not a fast problem solver, but I virtually always get the right answer because I solve problems with logic rather than visual intuition.
This is not visual thinking when you can not use your visual brain. From my perspective, it's just "thinking".