This is a 2005 Suburban, 4WD. When I drive for a while (e.g. on the interstate for an hour or so), then leave the interstate and start stopping at stop signs, etc. It will suddenly (totally all by itself), switch out of 2WD mode and into 4WD (high). When this happens, I cannot switch it out (back to 2WD), usually until the next day (i.e. drive it home, park it overnight, then it will switch back) – just stopping it and sitting there in Park with it off for a minute is insufficient. 
Our local friendly mechanic has already tried replacing the switch (suspecting a short), to no avail.
Crickets Is this too obvious or is everyone stumped? Kinda a let-down.
Anyway, it’s looking like the encoder motor - we replaced that and so far (4 days) have not had a recurrence. Hopefully that was it.
These electronically controlled transfer cases and axles are so Micky-Mouse in operation, the “systems” changed or were “re-engineered” almost every model year, field mechanics tend to shy away from fixing them or offering advice…You check the electrical connections, make sure switches are working, fuses, …After that, you are on your own…The factory Service Manual for your vehicle will have a troubleshooting chart…
Are you able to actually drive the thing home in 4wd? The truck should be basically impossible to turn on dry pavement if it’s really in 4wd-- it may just be an indicator problem or maybe only part of the 4wd system is engaging.
Unfortunately like Caddyman said, the days of 4wd systems being easy to diagnose went out with the old “move-the-stick” style ones.
In 2WD mode it drives normally. When it claims to be in 4WD mode, it is very difficult to make turns with: making a right turn at a 90 degree intersection requires a lot of gas, lots of jumpy resistance, and slipping tires, on dry pavement – if it weren’t actually in 4WD, then it wouldn’t be so important for me to figure out how to get it back into 2WD mode 
So I think it was actually going into 4WD mode; I certainly got repeated ‘breaking-traction’ on both of the front wheels (this is western PA, where there are endless bumps in the road and opportunities for the weeks to relieve their differences).
Caddyman’s points make sense to me – I hadn’t realized that was the situation. Hopefully the replaced encoder motor fixed it.