Cax"on n. A kind of wig. [Obs.]
Webster 1913
These days 'Caxon' is mostly found in dictionaries and the more boring sort of historical writings. Oddly, despite the fact that there are quite detailed accounts of dozens of types of wigs, there appear to be very few of the Caxon, modern dictionaries uniformly referring to it as a "type of wig" (usually noting that the term is now obsolete), or, in some cases, "A worn-out wig". You have to go back to the Brewers 1894 Dictionary of Phrase and Fable to find it described in even so much detail as "a big cauliflower wig".
To put this in context, it is fairly easy to find descriptions of a Ramillkes wig ("the queue was a long gradually-diminishing plait of hair tied with black ribbon bows above and below, or sometimes only below."), a Brutus wig ("a style of unpowdered, natural-brown and disheveled Scratch wig") and the Nightcap wig ("a close-fitting hairpiece with a short tail and small round head, named for its resemblance to a nightcap").
The first reference of the Caxon appeared in 1756, but perhaps the most comprehensive non-description is found in William Woty's 1760 poem, "The Caxon" (published under the pseudonym James Copywell of Lincolns Inn). At this point it appears that the Caxon was already an older, or at least more conservative, style of wig, and Woty presented it as an unchanging, universally acceptable wig fashion that would outlast the other foppish wigs of the day. The purpose of this poem was to mock modern wigs and those who wore them, and it is quite clear that he is also mocking the Caxon for being not-even-a-little-bit foppish:
For those [other wigs] require the wearer's nicest care,
The sport of ev'ry wind, and ev'ry drop
Of piercing rain, and flake of airy snow
To fluid crystals melting; and when night
Invites him to repose, then must they rest,
Or pendant on a peg, or soft reclin'd
Within the concave of inclosing Box,
Else all their fine oeconomy is lost.
Such caution does my Caxon never ask,
At all times uniform, whether on floor
Or urinal it lies, or 'gainst the cobweb wall
It hangs devoid of state, or whether Pugg
In dust-hole drags it for an easy bed,
Or chance may throw it careless in the street
To mingle with the chaos of a dunghill.
Nor does this Stranger to the comb of taste
Demand or oil or powder — need I tell
How, when I regulate its rumpled form,
I dash it on a post with stroke oblique,
Or full direct upon a table's verge!
The Caxon, William Woty, Universal Chronicle, or Weekly Gazette 2 (3 February 1759) 33-34.
Earlier in the poem he has specified that the Caxon does not have a 'cue' or a bag (bag wigs are a subject for another node, but basically the queue was encased in a bag... because fashion, that's why), and that it 'exposed the cheeks'. In contrast to Woty's description, by 1815 Richard Fenton and Samuel Rogers' description of an aged Caxon in Memoirs of an Old Wig indicate that it is an immense mass of curls, and in this case, one that had been added to many times over the years. The wig tells us that it had originally been constructed for a judge, but was also worn by lords and military officers (and, not too brag, but one must relate, a king).
In Legal Habits: A Brief Sartorial History of Wig, Robe, and Gown, 2003 (.pdf), Thomas Woodcock notes that "Caxon was the name given to any wig that had lost its form and design through neglect and exposure to all weathers." This may very well have been true throughout the use of the word -- I can't find any strong evidence otherwise -- but at the very least a Caxon was always rather generic form of gentleman's wig, perhaps most akin to what the modern reader might consider a barrister's wig.
While even the OED does not claim to know where the name Caxon comes from, mearly noting that it is most likely from the personal surname, Thomas goes on to state that "Originally a’ Caxton’, it took its name from the Cambridgeshire village of Caxton near to which a murderer who had disguised himself in a wig was hanged." I am suspicious of this etymology, but it is certainly more entertaining than having none at all.