Early matches for 'think tank' (or 'think-tank') in Google Books
Google Books finds several instances of this colloquial usage. The earliest is from H.A. Smith, "Shelving Versus Selling," in National Hardware Bulletin (November 1906):
It is strange that a hardware dealer is so perfectly satisfied when he gets his stock well housed and stored away in their little stalls. It is all right to look after the comfort of one's family or live stock and stow them away from the cold blasts of a cruel world. But a man who is keen to sell goods ought to work his "think tank" a little and study up a way to market goods.
From Harriet Comstock, Joyce of the North Woods (1911):
"And now," Filmer was drawling on, "while you and me are on this sort of house-cleaning spell, let me drop another item of interest into your think-tank. We-all up here ain't going to stand for any preaching business. I say this outspoken and friendly, meaning no ill feeling; just plain, what's what. You see them ideas of yours what you handed out last year set folks thinking. They sounded so blasted innercent and easy that we all chewed on 'em for a time, and some of us got stung. Now them as is native here can't think without suffering; and them as came here, came to get rid of thinking, and so you see none of us want to be riled along that line. See?"
And (as FumbleFingers notes in a comment above) from Elmer Ferris, "Crackers, Competition, and Automobiles," in The Outlook (October 26, 1912):
One point he ["Professor James"] made was this: He claimed that every man has got it in him to do something a mighty sight bigger than he's ever done yet, but the trouble is he limits himself in his own mind—sort of locks himself up in his own think-tank, see, and never goes any further. One reason why men get drunk is because alcohol kind of unlocks a man's think-tank and turns him loose and makes him see himself big. One man will think he's a captain of industry, and another one will think he's an orator or a singer, and, by George, that's probably what they really are, but o course alcohol paralyzes a man's action and blows off his energy like steam in the air and never gets him anywhere, and when he sobers up he finds himself back in the same old think-tank with his energy all gone and worse off than before.
From the context given, it seems fairly clear that both Smith in 1906 and Comstock in 1911 are using think tank as a synonym for brain; but Ferris in 1912 treats think-tank as something akin to drunk-tank—a mental prison cell where a man's thoughts are forced to dwell under restraint and lassitude.
Early matches for 'think-tank' (hyphenated) from Elephind
A search of Elephind newspaper results, however, sets the earliest matches for think-tank (with a hyphen) back to the period 1889–1891. From "Rather Severe Upon Royalty," in the Pittsburgh [Pennsylvania] Dispatch (February 13, 1889), reprinted from the New York World):
A statistician asserts that 20 princes and princesses of the reigning families of Europe have been treated for mental disorders. The nineteenth century has been very severe upon the royal think-tank.
From "The Supreme Court Decisions," in the [Indianapolis] Indiana State Sentinel (November 13, 1889):
This conclusion is bad enough for all practical purposes, In the face of the well-known constitutional provision that "all officers whose appointments are not otherwise provided for in this constitution shall be chosen in such manner as now is, or hereafter may be, provided by law;" but when the learned gentleman attempts to bolster up his erratic notion by citing as authority the fact that in some cases the legislature has provided for the election of state officers by the people, he simply makes manifest the defects in what Bill Nye would call his think-tank.
And from "Amusements," in the [San Francisco] Daily Alta California (April 21, 1891):
The story [of "The Woman Hater"] is a highly amusing one, and deals with the love affairs of Samuel Bandy, who is popularly known at his club as a woman hater, but who, as he confesses to his friend Dobbins, a retired coffee merchant, fairly dotes on the fair sex, and in consequence suddenly finds himself engaged to three women at the same time, without exactly knowing how it has all come about. He is mistaken for an ex-professor of philosophy whose "think-tank" is supposed to be disordered, and taken to a lunatic asylum on his wedding day.
Early matches for 'think tank' (unhyphenated) from Elephind
The earliest match for unhyphenated think tank is again associated with Bill Nye of the New York World. From "A Storage Think Tank," in the Omaha [Nebraska] Daily Bee (November 5, 1887), reprinted from the New York World:
Bill Nye in the New York World: In fact, Mr. Edison has now perfected, or announces that he is on the road to the perfection of a machine which I may be pardoned for calling a storage think tank. This will enable a brainy man to sit at home and, with an electric motor and a perfected phonograph, he can think into a tin dipper or funnel, which will, by the aid of electricity and a new style of foil, record and preserve his ideas on a sheet of soft metal, so that when one says to him, "A penny for your thoughts," he can go to his valise and give him a piece of his mind.
And from the New York Evening World (January 3, 1888), we discover that "Bill Nye's Think Tank" appears to have become a standing column title:
BILL NYE'S THINK TANK.
Painfully Shocked Over a Scientist's Alleged Discovery—His Platform.
I have been painfully shocked and disturbed by nailing tho following piece of information in one of my favorite newspapers: ...
From the Hazel Green [Kentucky] Herald (February 24, 1888):
Now "Cush," old-fellow, if you want to illustrate the prettiest spot on God's green foot-stool, and "write up" the best people under the broad canopy of high heaven, direct your steps hitherward, and do it on the double-quick, too. You can here find the readers of the Courier-Journal "food for thought" as long as they are possessed of a "think tank."
And finally, from "Will Morton Have a Say?" in the New York Evening World (November 22, 1888):
The "think tank" of President-elect Harrison is a queer receptacle. He has stowed away in it not only his own thoughts and ideas), but all of the thoughts and ideas of hundreds of Republican leaders and office-seeker on the subject of Cabinet material and other Presidential appointments.
It appears capable of receiving any amount of thoughts but refuses to be placed on tap for the benefit of any one.
Conclusions
There is considerable evidence for crediting Bill Nye of the New York World for the popularization of "think tank" as a colloquial term for "brain." He authored the first known instance of the term (in late 1887), seems to have had at least occasional recourse to the term as a title for his newspaper column Bill Nye's Think Tank (in early 1888), and was cited by someone working at another newspaper in another state as a source for the term (in late 1889).
And yet the odd fact remains that Bill Nye's first use of the term was in connection with a kind of artificial holding tank—a machine for recording and then storing thoughts automatically—being worked on by Thomas Edison. For this reason, both in the title and in the text of this first article, Nye uses the phrase "storage think tank," as though the basic idea was of a new kind of "storage tank." This same sense of "think tank" seems to be at play in "Bill Nye's Think Tank": I don't think he means "Bill Nye's Brain" here, but rather something like "Bill Nye's Thought Repository."
Still, by 1888—seventeen years before Etymology Online's estimated first occurrence of the term in the relevant sense—people seem clearly to have been using the term to convey the much simpler meaning "brain." As late as Harold Wentworth & Stuart Flexner, Dictionary of American Slang, first edition (1960), most people continued to use think tank in this sense. Here are two brief but relevant entries in that book:
think-box n. The brain.
...
think-tank n. = think-box.
But that older notion of think tank seems to have tanked since the emergence of "think tank" in the modern sense described in Merriam-Webster's Eleventh Collegiate Dictionary (2003):
think tank n (1890) an institute, corporation, or group organized for interdisciplinary research (as in technological and social problems) — called also think factory
At any rate, I can't recall having heard anyone refer to the human brain as a "think tank" in the past five decades. (By the way, Merriam-Webster's blithe association of the year 1890 with a term for which it gives a single, highly anachronistic definition seems to me to invite confusion; the dictionary could reduce the likelihood of misleading its readers by including the generally understood meaning of the term—as it was used between 1887 and the early 1960s—as a separate [and earlier] definition.)
Best Answer
Etymonline seems to be out of date here. The earliest examples in this sense are from before Valentino was even in a movie (at least according to the Wikipedia page linked in the question).
I found what looks to be a really early example from 1901:
The Oxford English Dictionary gives an example from 1912:
The OED also has an example from the 1923 LA Times referring to both men and women, but this doesn't seem to be the quote Etymonline is referring to either:
Also, Etymonline asserts that the first use of the word (in any sense) was first used in 1905, but the OED has an earlier quote from 1896 (albeit with a different spelling):
(Do note that "seksy" means "erotic" in the above quote as it is a different sense of the word.)