Crawl under and check out the transfercase, transmission, engine mounts, etc.
Make sure none are broke or loose.

Especially if you have a body lift on your Tahoe.

It could be that engine torgue is causing levers to hit the body or move enough to slightly engage the transfercase linkages.

 

do you have the new or old body style and its electronic switchs? honestly pulling the transfer case is relatively easy, you just have to remove both front and rear drive shafts, unplug the few plugs, drain it and un bolt it from the tranny, now if you unbolt it from the tranny, there is 2 places you can unbolt it from, on is an 8 bolt spot and the other is just 4, now if you unbolt it, always unbolt it from the 4 bolt section because if you want to replace the rubber gasket, its alot easy to find and install then the paper one involved with the 8 bolts, also the shaft gets guided on and off with the 4 bolt section which makes it easier to take off and reinstall, but id remove the transfer case and see if you can notice anything wrong, like fluid level, loose shaft of anything like that