As you point out, in the American Academy of Neurology Writing Styles And Standards Guide, available online at http://www.aan.com/globals/axon/assets/3078.pdf, there is the entry on page 11:
The word neurologic is preferred to neurological when used as an adjective.
I don't think it gets any more authoritative in this field than that. It is a preference, a style decision.
For what it's worth, we use neurologic in our veterinary publications, too. We consider it a style decision. When we copyedit manuscripts, we change neurological to neurologic (unless the word is part of a cited reference title, of course.) Neither form is "wrong," it's just a preference, and we try to be consistent.
We also use, for example, endocrinologic instead of endocrinological and radiologic instead of radiological.