I've had a similar issue with my 06. It was the rear axles seals leaking. They leak ever so slightly and it seeps into the park brake assembly on the inside of the rear rotors. The heavier load you pull, the stronger the smell. There were no drops onto the ground, just a very small streak on the rear hub.
Check the left frame rail roughly under the driver's seat, the front axle breather is located up there (follow the hose to the diff), and if you've been running in 4WD on moderate traction roads you may well have overheated the front diff and caused some oil to puke out of the breather.
These trucks are 4WD, not AWD and do not have a center differential so unless the road is *really* slippery things will bind up and overheat. I cooked my front diff driving an extended distance in 4HI in *6" of slush* on the highway, and slush is far lower traction than rain.
It is not a leak, it is overheating the front axle which cause some of the gear lube to puke out of the axle vent tube which is routed up into the left frame rail as I noted. I'd put 95% odds that this is what is happening to the OP, and it will ultimately result in a rebuild of the front axle if he continues using 4WD on high traction surfaces at speed.
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