well, I checked it out and got this explanation:
Finger: To pull your finger out is to hurry, to get a move on. This is another nautical saying and comes from the times of the Men'o'War. When the cannon were loaded a small amount of powder was poured into the ignition hole near the base of the weapon. In order to keep the powder secure before firing, a crew member pushed one of their fingers into the hole. When the time came for ignition, the crewman was told to pull his finger out.
There was no evidence offered for this, personally I'm even less convinced of this than of my garbled, half rmembered mill version. I have emailed quinion and hopefully he will help, though I have never had a query investigated before.