I just had this exact issue. Mine was a bit different. I was getting the 4wd service light while driving in 2wd on the highway. Not trying to select or anything. Then the Stabilitrac Light would come on. Everything would reset with no messages when I got in to drive it. Then would come back about 20 miles or so. Sometimes sooner.
I took it in to get looked into and they did a flash for a recall and another recall for the wipers. Said it fixed the issue. 25 miles into driving home it came back again.
I took it back, did't hear from them for 4 days so I called. Said they were installing a new Module (likely the TCU) but I didnt ask. When I picked it up they showed me that my issue was refered to FCs Engineering group for trouble shooting because they couldnt fogure it out. So they told them to swap the box after taking pin out readings and some where off.
The light is now gone. However, now it snowed a little so I wanted to put it into 4wd auto. Nothing just a blinking light. Tried in park, neutral, while driving on the fly nothing. Tried at a stop, 4hi, on the fly into hi nothing just blinks. Stopped tried 4lo, just blinks. This is were I am now. I will try again from 4lo first then cycle. But i seriously just got it back Tuesday, and started to search and found this post. I am glad the roads where not worse. I am going tobtry again. If it happens again, I am filming it, taking it back again for warranty work. I probably should have made a new post about this but I figured I would share in here what I got going on now too.