2000 VW Passat Wagon 4-Motion Engine Runs w/o Key

We have a 2000 Passat 4-Motion Wagon (automatic transmission) have had it in the family since it was new, it has 113,000 miles on it and we were always current on all scheduled maintenance, etc. The car recently has been doing something quite odd, hopefully some members can shed some light on it…

After driving, foot on the brake, removing the key from the ignition the car doesn’t turn off, the engine continues to run. When I lift my foot off the brake pedal, the engine goes off. With the key still out of the ignition, if I put my foot back on the brake pedal, the dash lights come on (as if the key was in and turned but not started). Lifting my foot off the pedal again the lights go out. After doing this two times, the lights don’t come back on and all appears normal. I have noticed it does this about 85% of the time now.

Any thoughts from the members here on what could be causing this, and a possible fix? Thanks.