Why does the light stay on?

Normally this website offers answers – but here is a mystery and a question …
I have noticed that when I park GBMINI#3 and switch it off, the “P” light on the automatic transmission stays lit:

Even after the lights are off and I get out, shut the door and lock the car, the “P” light stays on.
Some “running-in-and-out-in-the-cold” experimentation reveals that the light stays on for between 3 and 5 minutes. I have no idea why.

Any ideas?

First snow for GBMINI#3

Todays once-again-unpredictable weather system eventually rolled in tonight as freezing rain on the way home from work, and has now worked its way down to light snow and serious amounts of wind! The chrome mirror caps look cool covered in ice – but we will see if the doors open OK in the morning; supposedly the redesigned door handles address this issue …

Separate issue – I filled up last night, getting 351 miles from the first tank of gas. But it took 12.6 gallons to fill, and the range was still about 20 miles – looks like 0 miles range in this new MINI would be absolutely zero!
Apparently the OBC estimates are all much better than #2; my calculated MPG was 27.8 and the OBC was claiming 28.0 … good fuel economy while I still have to “baby” the engine 😉