Steve, check this out:

http://www.americansouthwest.net/arizona/grand_canyon/south_kaibab.html

It mentions parking for the South Kaibab Trail "along the highway by the turn-off". I used this parking area last May. It's a turn out almost directly across the hiway from the turn to Yaki Point Road which you would walk to the trailhead. There is room for about 15 cars . It also says it's .5 miles to the trailhead. That sounds about right although it always seems farther especially on the return trip (which you will not be doing). This parking area is right off the main hiway so I expect it is always accessible.