Are you saying that it's the cornering lamp that stays on ... or the turn signal lamp?
I've had an issue with my DTS where the left cornering lamp will not go off after completing a left-hand turn, but I will do a lane-change signal (where it flashes 3 times with the "bump" of the turn signal lever), and then the light will go out.
You can try to "reboot" the electrical system (if you haven't already done so). This will often resolve some of the little electrical issues. You might try it to see if that helps. I haven't had the problem since I've done this (I did it for another electrical issue, but ... happy accident ... cornering lamp is behaving (at least for the moment).
Quoted from SuperJim (as always, thanks to him for these instructions):
There is a way to REBOOT all of the electronic modules in the entire car.
Sometimes (lots of times) that will fix random electrical gremlins.
Remove BOTH battery cables... negative cable FIRST...
Touch both cables together for 5 seconds or so, making sure they have good contact with each other.
This will drain all the capacitors in the system.
While you have the cables off... undo the one bolted to the floor.
Take a little piece of sandpaper and sand the paint away from the attachment point.
It will then have a better ground.
Re-attach the battery cables... negative cable LAST...
You will have to do the window EXPRESS UP learn again and you MAY have to do the memory seat settings again.
Sometimes they will forget the seat settings and sometimes they don't.