A possible nautical origin
The (ever-popular) nautical origin should come, and go, first, not least because it also seems to be the earliest of candidates approximating the sense of the expression '[somebody would not be caught|seen|found] dead [doing something|being somewhere]' (hereafter WNCD):
Within a few cables of her lee-beam was the "light-green water, and the wind and swell setting her fast towards, it" Not a moment was to be lost. "Caught dead upon the weather-side of a reef," the ship "lay like a log upon the water." "Sail had to be made," he writes, "and way given to her before we could stay...."
(From A memoir of Capt. W. T. Bate, R. N., Rev. John Baillie, 1859. Emphasis mine.)
Here the sense is "without forward motion", "dead in the water", "unable to steer". While any sailor would loathe being so "caught dead", and the possible nautical origin deserves a mention, I have difficulty reconciling this 1858 use with the later sense of WNCD, not least because it expresses that something detestable has happened or might happen to somebody, while WNCD expresses the obverse, that somebody does or would detest something.
From that stopping point, my analysis becomes more tentative. Other than the negative element of the first finding, the following bulleted points are supported under the heading Evidence from press corpora, below:
- Although the WNCD expression was in use at least 32 years prior to 1900, none of the turn-of-the-century slang and dialect references I checked mention it.
- In my examination of popular press uses, the 'found dead' and 'caught dead' forms of the expression appeared earlier (1868, 1872) than the 'seen dead' form (1901).
- The textual evidence available to me indicates WNCD was probably originally an Americanism; the earliest instances I found are all from American sources. It should be noted, however, that my colloquial resources are predominantly American.
- No evidence indicates that 'caught dead to rights' sponsored the development of WNCD. Although 'caught dead to rights' appears earlier than WNCD, the first form of WNCD I uncovered was the 'found dead' form (1868), which does not fit with 'dead to rights'. One hybrid does appear, where 'caught dead' is used as an abridgement of 'caught dead to rights', but it appears at a much later date (copyrighted 1889). Additionally, the early sense of 'dead to rights' is the positive 'completely, certainly', which is at odds with the negative sense of WNCD.
- It is a plausible theory that WNCD is a semantic development of forms of the 'dead or alive' expression. The common collocation of 'dead' and 'alive' dovetails with the 'found dead', 'caught dead', and 'seen dead' collocations, semantically ("conceptually") and temporally. WNCD expresses the negative to a chorus of "found dead or alive" (beginning in 1828; this date and the next two from Elephind), "seen dead or alive" (1838), and "caught dead or alive" (1862); that is, '[I|he|she|they] would not want to be [found|caught|seen] dead [or alive] [doing something|being somewhere]'. (Note that the familiar "Wanted: Dead or Alive" is a later development--the earliest attestation in the Elephind corpus of popular press is from Australia in 1876.)
Dated lexical sources
WNCD is dated to the first half of the 1900s in The American Heritage® Dictionary of Idioms by Christine Ammer:
caught dead, wouldn't be
Also, wouldn't be seen dead. Would have nothing to do with, detest, as in I wouldn't be caught dead in that outfit, or He'd not be seen dead drinking a cheap wine. This hyperbole is always put negatively. [Colloquial; first half of 1900s]
(The American Heritage Dictionary of Idioms by Christine Ammer. S.v. "caught dead, wouldn't be." Retrieved August 17 2016 from http://idioms.thefreedictionary.com/caught+dead%2c+wouldn%27t+be.)
In OED Online, WNCD is attested from 1924-1966, and appears as
Colloq. phr. (I, etc.) wouldn't be seen (or found) dead in, with: (I shall) have nothing to do with (something or someone); (I) hate, detest.
["dead, adj., n., and adv.". OED Online. June 2016. Oxford University Press. http://www.oed.com/view/Entry/47615?rskey=WsH8K8&result=1&isAdvanced=true (accessed August 17, 2016).]
Observing that both the OED and AHDICA give the 'seen dead' form of WNCD, but the OED also gives only the 'found dead' form while AHDICA also gives only the 'caught dead' form, it seems likely that 'found' is the more likely idiom for the WNCD phrase in BrE, and 'caught' the more likely idiom in AmE.
Evidence from press corpora
All images (except as noted individually) are provided via Chronicling America: Historic American Newspapers, Lib. of Congress.
Early 'found dead' attestation:
(Memphis daily appeal. (Memphis, Tenn.), 10 Sept. 1868.)
(Evening star. (Washington, D.C.), 27 April 1870.)
(The New daily appeal. volume (Carson City, Nev.), 10 Sept. 1872.)
Early 'caught dead' attestation:
(The weekly Caucasian. (Lexington, Lafayette County, Mo.), 07 Dec. 1872.)
(The Ottawa free trader. (Ottawa, Ill.), 07 Feb. 1874.)
(Alexandria gazette. (Alexandria, D.C.), 17 July 1874.)
'Caught dead' as abridgement of 'caught dead to rights' (image from Google Books):
(From "The Autobiography of Joseph Jefferson", The Century, Volume 39, 1890.)
Early 'seen dead' attestation:
(The Kalispell bee. (Kalispell, Mont.), 11 July 1901.)
(The San Francisco call. (San Francisco [Calif.]), 11 Feb. 1913.)