From William Main Doerflinger, Songs of Sailor and Lumberman:
Until his advance, which usually went to his boarding master, had been worked off, the old-time sailorman felt he was "working to pay for a dead horse."
Stan Hugill is more descriptive. The first month's pay secured lodgings, an outift, and more practically, "booze and diseased harlots." The sailor considered the first month at sea a payless one. Hugill continues:
In the second dog-watch (6-8 p.m.) on the evening before the first day of the second month - i.e., just before they started working for "real money" - a canvas image of a horse with a rope-yarn mane and tail, stuffed with shavings and some holystones for weight, would be hoisted to the main yardarm to the singing of this shanty...
Doerflinger also describes the British payday custom of parading a stuffed scarecrow horse around deck, hoisting it to the topmost yardarm, and cutting it adrift. The lines about the old man and his horse, he writes, come from the minstrel song "Clare de Kitchen".
Masefield gives a nearly identical shanty called "Poor Old Joe."