Four wheel drive

No, the case itself does not control the lights, they are controlled by the encoder motor on the case as well as the transfer case control module. Both are common failure items. The fastest way to determine which is the problem is actually to use a good scan tool to see what the various parts are doing as you move the selector switch. It will show you which mode the case it is in as you move the switch, or show you that is is not switching as you move the switch. As those parts can be very expensive and need to be programmed to work, you do not want to just guess and replace them hoping you find the correct one the first time.