"There's one more thing, I got the pink slip daddy" In 1963, the title of a car in California was printed on a pink piece of paper.
Challenging someone to a drag, if someone said "I got the pink slip" it meant he was betting the ownership of his car on the outcome of the race.
Perhaps, but not the explanation I head about 45 years ago:
Lots of hot rod donors from the 30's and 40's might have been resurrected from the wreckers or found essentially abandoned - so not so quick to get a title. Hot rodders, being mostly kids would concentrate on hopping the thing up before dotting the "i"s and crossing the "t"s when it came to registration. Later it would be easy enough to fall afoul of the law and lose the car. In this case the singer's stating that in this case, it's owned outright and legally.
