Any parking mechanism depends on power being supplied to the motor after you turn off the supply. This drives the motor until the wiper breaks the contact by moving into the park zone. I suspect that there is a wrong or missing connection.
I'm not familiar with the wiper system on your car, sometimes the parking works by switching the earth, sometimes the live. If it is earth switching it will not be obvious that there is a missing connection to earth.
Alternatively, I believe the supply to the wipers depends on both the headlamps and the windscreen wipers being activated. It may be that you have live supplies from both of these systems but no permanent live. Therefore, when the headlights and main wipers shut down, there is no live supply to make the headlamp wipers park.
Hope this helps.