I think some are overthinking this.
With the exception of
@SAJ who's hauling livestock/horses.
If you use ON or AUTO and cruise, the truck will maintain your speed using the EB and as needed, the trailer brakes if equipped.
If you want more aggressive downshifts, and/or later upshifts, use TH.
Some say TH locks out 6th gear and that's just not true. I can run in TH in 6th pulling 16K on the flats, it just downshifts more often so I usually reserve it for the big hills.
You may find the downhill shifts more abrupt if the speed is allowed to climb before it engages.
If you want more control using your right foot and gear lockout, use EB ON.
DIESEL EXHAUST BRAKE — ENGINE BRAKING (IF EQUIPPED)
The purpose of the exhaust brake (engine braking) feature is to supply negative (braking)
torque from the engine. Typically, the engine braking is used for, but not limited to, vehicle
towing applications where vehicle braking can be achieved by the internal engine power,
thereby sparing the mechanical brakes of the vehicle.
Benefits of the exhaust brake are:
Vehicle driving control.
Reduced brake fade.
Longer brake life.
Faster cab warm-up.
The exhaust brake feature will only function when the driver toggles it on by pushing the
exhaust brake button until the “Exhaust Brake Indicator” is illuminated. Normal (Full Strength)
exhaust brake mode is indicated by a yellow “Exhaust Brake Indicator”.
Once the “Exhaust Brake Indicator” is illuminated and the vehicle is moving faster than
5 mph (8 km/h); the exhaust brake will automatically operate when the driver removes
pressure from the accelerator pedal. Exhaust braking is most effective when the engine RPM
is higher.
The automatic transmission will downshift more aggressively in TOW/HAUL mode
when the exhaust brake is enabled to increase brake performance.
Do not use the exhaust brake feature when driving in icy or slippery conditions as the
increased engine braking can cause the rear wheels to slide and the vehicle to swing
around with the possible loss of vehicle control, which may cause an accident
possibly resulting in personal injury or death.
NOTE:
For optimum braking power it is recommended to use the exhaust brake while in TOW/HAUL mode.
The exhaust brake feature can also be used to reduce the engine warm up time. To use the
exhaust brake as a warm-up device, the vehicle must be stopped or moving less than 5 mph
(8 km/h), the "Exhaust Brake Indicator" must be on, and the coolant temperature must be below
180°F (82°C) and ambient temperature below 60°F (16°C).
Automatic “Smart” Exhaust Brake
Automatic “Smart” Exhaust Brake technology delivers smoother, less aggressive exhaust
braking characteristics during downhill descents. Although it can apply full exhaust
braking force if needed, Automatic “Smart” Exhaust Brake may not apply obvious braking if
the vehicle speed is not increasing. Automatic “Smart” Exhaust Brake is intended to maintain
vehicle speed, while Full Exhaust Brake is intended to reduce vehicle speed.
Automatic “Smart” Exhaust Brake can be enabled by pushing the exhaust brake button
(on the center stack) again anytime after the normal Full Exhaust Brake has been turned on.
The “Exhaust Brake Indicator” in the instrument cluster display will change from Yellow to Green
when Automatic “Smart” Exhaust Brake is enabled. Pushing the exhaust brake button
again will toggle the exhaust brake mode to off.