I understand, but the parking lights are not tied to the ignition, and accidentally hitting that switch and asking questions about lights being on is one of the most common Subaruisms in the known universe. Dealers actually cover it in the delivery speech so they don't get quite as many calls on it.
Do the front markers stay on as well?
If so, it is the parking lights and the switch is on top of the steering column.
Have you checked that switch?
If that is not it than you have a very unusual short on the hot side between the always on 12V and that circuit, probably under the dash or in the column.