If I where you I would "pretend" that you want to return the car, and do some play acting here
and hold out until they offer you a $1000 discount and then finally "cave in" and accept. But I assure you they are making at least a $4000 profit on the car and that $1000 would look alot better in your pocket than in theirs.
And that car is a sales dog so I seriously doubt they will just let you walk out the door over $1000.
Now the trick here is to act like you want to return the car and that your mind is made up. You will have to do some Hollywood acting here. And dont ever let the number $1000 come out of your mouth.....if you mention "$1000" they will know that you are acting and will call your bluff. You must pretend in every way that you just want to return the car and you wait until they offer to discount it to $1000 or higher and when you hear that magic number thats when you say "okay....
EDIT: THe fact is you did some lousy negotiating from the outset (for agreeing to 12,000 in the first place) so you should count your lucky stars that you have been given a second opportunity to rectify a past mistake. Believe me that very few times in life do we get a second chance to correct a past wrong.