Pedantic point of maritime work song order: It would serve as both ceremonial forebitter and halyard chantey when used to hoist the horse.

Believe it or don't…Am I flogging a dead horse...?

The effigy was often illuminated with a signal flare (blue light) and dropped after sunset. The 'auction' bits were an old time side “benefit” (ie: modern day tip or gratuity.)

Long post:
“Monday, March 3.— We had this evening what to the sailors was evidently splendid fun, and what to the emigrants was at least a novelty. An auspicious ceremony, known to seamen as “Flogging the Dead Horse,'” has been performed. For the benefit of the uninitiated I explain. When the crew for a vessel are engaged, the owners allow them to draw the first month's wages in advance ; and those who know our sailors best will be disposed to believe that not a great amount of the “advance” remains in hand when eventually the crew ship them- selves for the voyage. The sailors regard this first month's work as a sort of nightmare—the sooner it is over the better they like it. And when the month is up, and their wages commence to accumulate, they celebrate the occasion in the manner I am about to describe. Well, this day completed the first month of the sailors' service ; and they manufactured what they called, and what for courtesy's sake I will also call, “a horse.” There was no nonsence about this said gallant steed. I cannot exactly allude to its fiery eyes, or to its dilating nostrils—for the simple reason that it had neither. I may safely speak as to its mouth and jaws, and will be well within the mark if I assert that never before in my life did I witness a horse with such a magnificently concocted pecking machine. The carcase was fearfully and wonderfully made. Some canvas which had done service for our good ship for the past three years, was first sewn into shape, and by dint of much intricate work and delicate persuasion, the internal organs, in the shape of shavings and hay, were artistically inserted. The assistance of a pseudo veterinary surgeon was then called into requisition, the needle and thread were applied, and the carcase stood forth a completed thing. And it was a sight to behold. Its arched neck, the gracefully-curved back, the handsome rise of the haunches, and the prettily-rounded turn given to the posteriors— these, brought to a climax by a tail of flax of magnificent proportions, were, as I have intimated, a sight to behold. But the sight of all was the gallant charger's legs. They were none of your thin-ankled, slimly-built, tapering legs. They were good, genuine, stout, all-straight-down-alike, such as would have graced the most elephantine of elephants, or even that much maligned gentleman (late of Dartmoor) the Claimant himself. Legs, the joints of which were never likely to get out of joint, with hoofs such as horse or effigy never possessed before, and, I am inclined to think, may never possess again. And now you have the horse before you —

        'Twas not a form that the artist calls fine;
        'Twas not a form in the classical line;

But it was a decently-rounded conglomeration of hay and straw, canvas and sailors' breeches, honestly manufactured, and a legitimate outcome of the united intelligence of half a hundred Dutchmen and Englishmen. My sense of admiration was so overpowering that serious thoughts possessed me of driving a bargain for a purchase of this exquisite work of art, with a view of presenting it as a souvenir to one of our museums; but the idea was evanescent. A programme of other and more serious work was chalked out for the interesting creature. The shades of evening were approaching, and with them there came the sounds of laughter and revelry. From the forecastle there emerged a roaring procession of Englishmen, Irishmen, Scotchmen, and Dutchmen—sailors, cooks, stokers, engineers, and emigrants. In their midst, bound around its neck with a stout rope, they dragged the unhappy effigy of their own creation, and even as Macbeth's witches marched around the seething cauldron, so even marched my heterogeneous procession round and round the ship, chanting to a horribly flat minor key—
        Poor old man, thy horse will die —
                Poor old horse.
        And when he dies we'll tan his hide —
                Poor old horse.
        Poor old horse, thy days are ended —
                Poor old horse.

Having repeated the chanting of this elegant piece of poesy for half an hour or more, the procession wended its way to the foremast, which one of the sailors mounted, carrying with him a line attached to the “poor old horse.” Amid the united “hurrahs!” of the English, Irish, and Scotchmen, and the deep-toned “Hoerá's!” of the Dutchmen, the effigy was then hauled up to the yardarm. Sundry invocations to the publican's 'spirits" were offered up at this solemn juncture; and presently, accompanied by a final roar of merriment, the line attached to the executed "old horse" was cut, the effigy fell with a loud plunge into the sea, and in a few moments the 'horse" was lost to the sight of mortal man for ever. It was a scene calculated to arouse a man's moral faculties, and I fell to sentimentalising. The conclusion arrived at was, that as the “horse” had become food for fishes, I could do little else than pity the whale or any such other monstrosity who, mistaking the Dutchman's Stad Haarlem* “horse” for a real dead one, swallowed it under the delusion that it would afford a wholesome meal. I will venture to predict that that veritable whale will suffer from periodical attacks of indigestion during the next half century.

The upshot of all this mummery was that we—the saloon passengers—were " respectfully invited" to stand glasses of grog all round to the crew. It was not within the power of human nature to withstand such an appeal, so sundry bottles of whisky were subscribed for, and glasses were ordered. It is due to the Dutchmen to add that they swallowed the “real Dublin” with as much gusto as if it were goodly Scheidam, while the English fraction of the crew did splendid justice to the reputation they bear of knowing how to get outside of a capital “dhrop o' the cratur.”
[Old England and New Zealand, Simmons, 1879]

*Barque rigged auxilliary steamer S.S. Stad Haarlem (1875) at Rootsweb.