First, consult the owners manual. It tells you when to use Tow/Haul mode and when to use M mode.
My wife in an engineer at GM now. I would not take her advice on towing from her, nor from that retired one.
Manual mode is nothing like manual gear selection. It just limits the automatic shifting of gears to never exceed the indicated gear. If the truck is in M5 going 30mph, you aren't actually in 5th gear. 3rd probably.
You won't want to tow under 2000rpm. The 6.0L doesn't have much power below 2000rpm. While it is plenty for an empty truck/van, not when when you double the weight the engine is trying to move. I like Tow/Haul mode and M5 most of the time when towing my TT. I like to stay between 2000rpm and 4000rpm most of the time. Peak torque of the 6.0L is over 4000rpm and it seems to wake up over 3000rpm.
Use tow haul mode any time you tow your TT. The pennies you may save on fuel will be blown on transmission repairs.
