From my perspective, my eyes are constantly roving, but I have no idea how it looks from the outside, no idea if it's noticeable. I'm not much of a counter just for the sake of counting, but if I see numbers, I start doing little math operations on them, adding them, dividing, that type of thing. It's really irritating when I have something I should be focusing on because my mind is constantly manipulating the numbers whether I want to or not. And when there aren't numbers, I do similar things with words and sentences. For instance, looking at a sentence on a billboard, I end up counting the letters and spaces so I can find the figure or space that is the middle of the sentence, the fulcrum of symmetry if you will. Or if say a sentence has an odd number of words, like 3 or 5, i cut the sentence in half and count how many letters I'd have to add to one side or the other to make them symmetrical. In case you didn't notice, I have huge issues with symmetry and constantly striving to achieve it in everything I observe. But to answer your last question, no I don't expend effort trying to control my eye movements, unless there is something specific I should be focusing on. For me, its kind of a mental stimming when I'm out in public, it's a lot easier focusing on random letters and numbers than the people around me.
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Your Aspie score: 181 of 200
Your neurotypical (non-autistic) score: 40 of 200
You are very likely an Aspie
INTJ
What's the difference between ignorance and apathy? I don't know and I don't care.