You have to know for certain if you have an external exhaust brake or if your braking is a function of the variable turbo vanes, this info should be in your engine owners manual . I'm not certain what year Cummins made the switch.
If you have the external exhaust brake , the control is an air solenoid, that has 2 functions, 1 allow air pressure to the actuator to close the flap in the exhaust pipe , and 2 vent the air pressure from the actuator, to allow the internal spring in the actuator to open the flap in the exhaust pipe to allow normal engine operation. If lubing the mechanism doesn't help the operation, check the ground wiring on the air solenoid if all ok then you may need a new solenoid.