Taking the trail that branches off right immediately before the gate leads one past Freel Peak, & eventually to Armstrong Pass, where it meets up with the Tahoe Rim Trail. The Tahoe Rim Trail (going L at the junction) then goes across the slopes of the mountain itself, going up a heinous number of unnecessary switchbacks, before finally attaining the saddle mentioned in the route description. This variation (i.e. taking the trail) adds at least another 3 miles to the outing (to the suggested 5.5 round-trip). We had to turn back at the saddle due to not allocating enough time.
Taking the private road, on the other hand (instead of the trail mentioned)... things suddenly make much more sense (as discovered during the descent)!