My LLY gauges did that, but I did not have any CELs or system messages.
The instrument cluster stepper motor was going out, which I replaced. I believe that there is a bulletin from GM that describes the problem.
My LLY never threw codes or gave a CEL when I blocked the EGR.
Also, I have towed hot and heavy, and have never had an overheating issue. The fan came on a time or two when the truck was still stock, but nothing since I made exhaust and intake modifications and ran a decent tune (first the...
You may find the information in this link helpful. The general rule is to shoot for a rim width that is around 70% of the tire section width.
http://rimringz.com/pages.php?pageid=53