[hollerith]

>you have to also figure out where the mouse pointer is, and then start the mouse moving in the right direction

Although it can be tricky to know what is actually going on during a "non-deliberative" task, I am fairly sure I start moving the mouse, then my brain's motion-detection circuitry very naturally tells me where the cursor is.

One of the reasons I believe that is that I remember a few times choosing (or noticing that I prefer) to make a vaguely semicircular arc rather than abruptly reversing direction. (If I did what you describe, I would probably not have reversed direction often enough to have such memories. In contrast, if I'm right, then I would've reversed direction half of the times that I had no idea initially where the cursor was relative to the target.)