while it seems to imply having your finger up your bum, I've never had the faintest idea why anyone might do this. Personally, I am quite capable of doing nothing without resorting to such contortions. Anyone know?
There was another old RAF saying about a layabout in which he was said to have "His thumb in his bum and his mind in neutral". Clearly, the notion - whether involving finger or thumb - was that he was somehow pleasuring himself instead of working! I'm not too sure about the apparent 'gearstick' connection!
I think the implication is : If you have your finger up your bum it extremely limits movement or ability to do anything else. Therefore, by removing digit it frees you up to perform other and more useful tasks. I do not speak from experience of course nor can I prove this theory.