Whence "funicle"? Let's see what we can figure out.

My CD-ROM edition of the American Heritage Dictionary—which offers some neat search functions—lists 405 words or terms ending in "–ical," from "acoustical" to "zoological." Most, if not all, of them are adjectives. It lists only 31 words or terms ending in "–icle," from "air-cushion vehicle" to "vesicle." Most, if not all, of them are nouns. Therefore, I conclude the ending should be spelled "–ical."

Now, if you examine the words ending in "–ical," you can see that in a large number of cases (but not all), the root is a noun ending in "y", and that the "y" was replaced by "ical" to convert the noun to an adjective:

Astronomy - Astronomical
Biography - Biographical
Category - Categorical
Economy - Economical
History - Historical
Philosophy - Philosophical
Symmetry - Symmetrical
Tyranny - Tyrannical
...plus all the words ending in "–ology":
Biology – Biological,
Criminology – Criminological, etc.

Now, the expected root, "funy" doesn't exist—but we would expect that only if we assume "funical" is the correct spelling. What if it were "funnical"? Then the root would be "funny." At last we have arrived at a plausible explanation of "funnical": it is derived from, and apparently means, "funny." The derivation is irregular only in that "funny" doesn't need to be converted to an adjective because it already IS an adjective. But that's logical enough, I think, for a word that was meant to sound funny in the first place.