It's not the parking light function? Turn the engine off with the indicators set left or right and the appropriate side indicators stay on. (At least on some cars)
If the light warning light came on your dash then its a sidelight bulb gone, more likely same side that the indicator is permanently on. Happened to me this week.
Have your LCM and GM5 check..sometimes when it goes undervoltage..it corrupts. Symptoms (indicator still on even door armed). Happened to my bimmers. But then sometimes it function normally by luck.
The batteries dead now as i left it overnight and havent had time to go near it. Will get her going this weekend for an investigation, hopefully some jump leads and a frankenstein moment later we'll get to the bottom of it.