I must have seen it in the past and thought it an error, until today, when it appeared in such a very correct context, that I had no choice but to take it at face value. It appears in the title of THE book on Academical Dress of British and Irish Universities, whose existence I was alerted to by makyo.
Clearly, it is a correct word. Is it just a British Isles term? Would it today be considered old-fashioned?
I started off my research in a very superficial way: I put the term into Google. 714,000 hits, but Google's source of word definitions does not acknowledge the word as an established on. Google's a US company. Does it use a US dictionary for searches from its UK site too, or is the word just rather rare?
The OED was, unsurprisingly, more forthcoming. The earliest known instance of academical was in the same year as the earliest known instance of the word academic (1587). It does get used to refer to many of the same things that academic is used for - but the two adjectives are not entirely congruent. academical is more likely to refer to an academician - as opposed to an academy - and, most relevantly, academical specifically refers to academic regalia. (From 1823 - "Young man, how dare you be without your academicals!") The OED pays heed to its natal institution, including amongst the established uses of the term the position of "academical clerks", effectively work-study positions available at some of the Oxford colleges.
Even if it still sounds unexpected to my ear, I am now at peace with single term, academicals, for academic regalia. Good enough. But I am still unsure if this is a word in modern usage beyond the numerous university-based societies which have ensconced it in their names.