Why do the parking lights stay on after locking

Sounds like your cars security system thinks someone is trying to take your car or trying to tell you the car is not fully locked up?
Here a few ideas
_Is your car parked on a hill? Your car thinks it is being towed away!
-Another thought is that when you lock the car, one of the doors or a hood is not fully closed and the car is telling you the car is not securely locked up?
-Is your car in park when you lock it. If not it may be telling you it is not in park?
-Did you leave a set of keys in the car?
-Did you leave the lights on?
-I know when you fist go your car after being parked for a time and you see the alarm light flashing, it indicates someone tried to open your car. Did you go back and check the car was locked and activate the security system?
Let us know if this helps.

which light?
just reverse,
and not stuck in park/neutral.? (called park lock out) in USA.

I have had the parking lights on my 1998 forester stay on w/ no way to turn off. Used the remote door lock to lock and unlock car and the lights went off?????????? This has happened twice with the same solution

Do you have a separate parking brake light and a "regular" brake light? Most vehicles only have one light, it illuminates when the parking brake is set, but it also illuminates when the system detects a failure anywhere in the brake system.

You could have a separate light for the anti-lock brake system (ABS ).

Your description of a light that is on till you apply the brakes is usually a sign of some sort of system brake failure. Start with brake fluid level, then inspect the brakes at each wheel, looking for a leak.

If nothing detected there, then you likely have something more serious. (Master brake cyclinder bad, possible something in the ABS brakes, etc.)

Others may disagree, but I would suggest not driving the vehicle (except to a mechanic) until this is corrected.

My 2006 Uplander would not shut off the parking lights. I came here for a solution. I saw the answer here, actually the question, and I used the key fob to lock the vehicle. The lights went off. That was a temporary solve. Now, is this a "glitch" or a "feature"?

MAKE SURE THE INDICATOR STOCK IS IN THE OFF POSITION WHEN YOU LEAVE THE VEHICLE AS THIS KEEPS THE PARKING LIGHTS ON IN THAT DIRECTION.GOOD LUCK.

Security is your problem (like for MANY others... me included). There is a detailed write-up here: http://vatspasskey.com . The guy is great, this was the only way I was able to save my 94 Park Avenue.

Could be brake light switch

The park lights staying on indicates the switch is deteriorating.
I would replace it.
The door locks is probably a voltage issue. With the cold weather, the locks need more voltage to unlock. They get that voltage when the engine is running. If you really want the locks to work without the engine, you might try accessing the locks and cleaning them. Then use a lightweight grease, like lithium grease, to help them open with less power.

Have the brake lights checked to verify they work, if they are not working the system will stay locked in park, most likely the problem is a degfective brake light switch.