Just to add to the confusion there is this.

Gotta haul that timber 'fore the sun go down
Get it cross the river 'fore the boss come round
Drag it down that dusty road
Come on Jerry let's haul this load

Timber holler Timber
Cuz oh that timber gotta roll.

My old Jerry was an Arkansas Mule
Been every where and he ain't no fool
Weighed nine hundred and ninety two
Done everything that mule can do.


etc.

So we have a mule and we have a man hollering timber and still no explanation of Mountain jack. Mule skinners were the ones driving the mules right? So they would not be lumber jacks. Yet here is one hollering timber. Why is that?

Well that enough speculation from me.