I'd Bet That You Need To " Service Four Wheel Drive " .
" The light had been steady . . . "
Is the light still on or did it go out ?
There exists a GM Technical Service Bulletin, written for GM technicians, that pertains to 2007 Chevrolet Avalanche, Suburban, Tahoe, and 2007 GMC Yukon, Yukon XL models with NVG246 Transfer Case (RPO NP8).
The bulletin discusses an intermittent " Service Four Wheel Drive " message and a DTC (Diagnostic Trouble Code) CO378 set by the TCCM (Transfer Case Control Module).
The bulletin advises technicians to check specific terminal pins in a specific connector at the TCCM and to update the TCCM with the latest calibration.
Also, it advises that the vehicle should normally be driven in 2WD mode and to use Auto or 4WD modes when road conditions are appropriate.
Rocket science ? No, but it's close. If your problem is intermittent and has CO378 set then your TCCM unit may need to be reprogrammed as outlined in the bulletin. Otherwise, it will have to be properly diagnosed (Probably starting with a code scan) by a rocket scientist or mechanic who understands this stuff to find out what went kaput.