Where did the word or game padiddle come from?

The following site does not give an explanation of where the name came from but does explain the game, or at least one version of it: - http://www.urbandictionary.com/define.php?term=padiddle THE PADIDDLE GAME - A "Padiddle", as any trucker will tell you, is a car with one light out. The first person to see one, calls out "Padiddle"; the person who spots the most wins.
Car Padiddle - 1 point
Semi-truck Padiddle - 2 points
VW Bug Padiddle - 3 points
Taxi Padiddle - 5 points
Farm Equipment Padiddle - 5 points
Boat Padiddle - 5 points
Train Padiddle - 10 points
Helicopter Padiddle - 15 points
School Bus Padiddle - 20 points
Police Padiddle - 25 points
Airplane Padiddle - 100 points

http://www.angelfire.com/vi/thevixenvault/definitions/definitions.html
PADIDDLE/SPADIDDLE/SPADOODLE(exp.&n.): A double-meaning term, partly describing the reaction to be shouted in accompaniment of quickly striking the roof of the automobile in which the exclaimer is physically situated, this act is to be carried out upon the viewing of another automobile which, tragically, is missing the illumination of a least one front headlight or foglight. Also describes the title of the game which dictates that these actions must be taken (preferably rapidly and with vigour).
ELDDIDAP(exp.&n.): similar to a padiddle* but is solely employed when a light on the back of an automoblie has been broken, burnt out, or otherwise extinguished. In this instance, though, it is imperative to hit the floor instead of the ceiling.
NIDIDDLE(exp.&n.): the state of an automobile when a light previously upon it has been entirely removed, socket 'n' all! Can be played in conjection with padiddle/spadiddle/spadoodle*.