Sorry to bring this topic back up from the dead, but I have a similar issue - headlights, brake lights, and dome lights dimming from a cold start only. They stop dimming after 10-30 minutes of driving.
I've used a multimeter on both the battery and alternator under both conditions
Battery while lights dimming: 12-14v
Battery while lights steady: 12-14v
Alternator while lights dimming: 3-4v
Alternator while lights steady: 11-14v
So I think it's the alternator, but one thing that's giving me pause is that it was replaced recently. January 2016, per the Carfax, just a few months before I bought the Suburban, and it does look new. Of course it's entirely possible that the replacement alternator is defective. I took the S-belt off and spun the pulley, there is no play or noise.
Before I spend the money on another new alternator, does anyone have any suggestions? Thanks!
Edit: I took the plunge and bought a new alternator for $150. It fixed my problem - the old alternator was putting out inconsistent voltage.
For what it's worth, I bought a 160 amp because I had an RPO that called for one. I have no way of telling for sure but I suspect the old one was a 145 amp.