Got me? That's why I ask. Logic seems to say none and I admit not following the reasoning but my search of towing TJ with an Aussie locker turned up some of the problem responses:
The transfer case, np231 in the neutral position connects both the front and rear driveshafts so that they are turning at the same speed. The transmission is the only thing that is left disengaged. With the aussie lock installed and the front driveshaft connected to the rear, when your entering into a left hand corner, the left front wheel will not want to slow down and will essentially get pushed through the left turn straight. At a certain point it then will turn to the right, ie wrong way, and cause all kinds of bad things to happen. Don't ask, been there done that already.
On right hand turns, the left front wheel is basically brought along since the right front wheel is able to slow for the turn, the left just comes along with it. But basically, your right front wheel is free from all the rest of the drive train because of the split axle. With out the spider gears in the front axle the left front wheel it tied directly to the rest of the drive train and even though the locker is working properly, when the right half of the axle is not engaged there is nothing putting pressure on the locker to have it unlock.
One way you can test this is to simply hook up your Jeep in 2wd and put the tranny in neutral. Pull it around the block or whereever for a short distance. It will tow just fine. 2nd check is to start the Jeep. Put it in 4wd, to engage the front axle, turn the Jeep off, so that the axle is still engaged. Then put the trany in gear and the transfer case in neutral, and tow it around the block ect. Both of these methods will make it turn to the left just as it would without the locker, although the second method will tend to scrubb the tires a bit more than the first since it will be relying on the locker to release instead of the split axle.
I hope this makes sense to you. It took me some serious head scratching to get this figured out.
When I tow for long distances, I simply remove the front drive shaft and everything is good.