Just to finish beating that dead horse I googled and figured a few things and this is what I got:
Tag axle alignment effects:
Standard perfect alignment is with all wheels rotating on circles centered on a single point. The tie rod and crank arm geometry cause the turned wheels' axle lines to intercept at a point on the line that goes through the rear axle. Note that a degree or two of toe-in would make the angle formed by the front wheels' axles narrower and move the apex further away and behind the axle. A degree or two of toe-out would open the angle formed by the front wheels' axles while moving the apex in closer and in front of the axle. A car I fiddled with was harder to turn when it had toe-in and hard to keep straight with toe-out.
There might be a picture at http://langexkft.eu/angol/services/a_wheelalignment.htm
On a lego website http://sariel.pl/2008/12/8-wheeler/ there is a diagram of a 4 axle truck:
The centerline between the two axles is shown as the line the apex would be on for perfect alignment. So, if a tow vehicle had some toe-in based on the original axle it would be like having less toe-in when the tag axle was added. I expect then that there would be a little less stability with the tag axle added and no wheel alignment changes.
An alternative source of instability for short wheelbase tow vehicles would be the high nose effect when power is applied. During high speed towing the nose may be constantly raised so that the tie rod ends are deflected downward and the net effect is like shortening the tie rod to create toe-out. It may be what causes the dramatic swaying and roll-overs of some tow-trailer combinations. A tag axle geometry could help keep the tow vehicle level, maintaining the best steering geometry.
Some of the numbers involved are these:
2012 Liberty wheelbase: 106.1 inches
2012 Liberty track: 61 inches
2012 Grand Cherokee wheelbase: 114.8 inches
2012 Grand Cherokee track: 64 inches
Liberty existing wheel approx. 30” OD
Liberty clearance under tail approx. 17” (say 16” OD)
With 4” tread-tread, ctr-ctr = 15+4+8 = 27”
Half would be 13.5”
Added to the Liberty wheelbase it would become 119.6”
Wheelbase ratios: GC/Lib=1.082, LibTA/GC=1.042, LibTA/Lib=1.127
Small tire capacity: ST175/80D13 is about 24” OD and should hold 1,360 lbs each
I'm not the guy who can build a tag axle for a jeep especially if I'm getting my info from lego builders, but I wish I could buy one. A normal person would just buy a bigger tow vehicle, and it's likely I will do that, but I'll have to drive that bigger vehicle for the 350 days a year that I'm not towing anything. The big well equipped trucks also come with a lot of stuff that I don't think I'll need ever really.
That's it I guess, thanks for the efforts, guys, as always.