I once tamed the sway of a long sailplane trailer which I towed with a short tug. (Bronco-II) In the process, I looked into the sway issue a great deal.
One point few consider is that with a rear bumper (vs. 5th wheel) tow point, the trailer can and does apply steering force to the tug whenever two are not aligned. This is because the the tug’s rear wheels serve as a fulcrum, and the farther the ball is behind the axle, the more leverage it has. When the ball is located over the axle (5th wheel or goose neck) then the trailer has no steering leverage on the tug, and that point of interaction is eliminated.
Another point that doesn’t get enough attention, is that when braking, the trailer is pushing the tug. The steering effect mentioned above causes the trailer to steer the tug in the direction the exacerbates the misalignment. So a heavy trailer can jack-knife a light tug when braking no matter how it is balanced, depending on how far behind the rear axle the ball is. Having brakes on the trailer is very helpful in this regard. Applying trailer brakes can even stop sway due to other reasons. Without trailer brakes, applying the tug brakes once a sway has started often results in immediate jack-knifing.
But to the OPs question regarding tail heavy vs. hitch heavy :
Consider the trailer going around a modest curve…
If the sideways force due to radial acceleration is balanced in front of, and behind the trailer axle, then it produces no steering couple.
If the front is heavy, then the trailer tend to steer toward straight ahead. You could say that the hitch-heavy trailer “wants to” go straight AKA understeer.
Now make the trailer tail heavy. There is now more lateral force behind the axle, which tends to turn the trailer into the curve. Once it starts turning, it “wants to” turn sharper.
The hitch heavy trailer exerts force on the ball that tends to steer the tug into the turn. (oversteer)
The tail heavy trailer exerts force that turns the tug the opposite way. (understeer)
If the tug is light and the hitch moment long, then the hitch-heavy trailer can still cause trouble, because even though the trailer is stable, it causes the tug to oversteer.
The tail-heavy trailer is totally unstable without the tug. If the trailer is light, and the tug quite heavy, it might not become unstable until very high speed.
The above is looking at the forces during a constant radius curve. As the radius changes or reverses, dynamic forces come into play that cause the situation to be far harder to analyse and explain.
Now if that isn’t enough, the height of the load in the trailer causes it to roll side to side. The usual leaf springs on the trailer then convert this rolling in to steering of the trailer axle.
One interesting device that helps a lot with trailer sway is the sway-brake friction device. The adds a great deal of friction to the coupling in the yaw axis. The friction forces tend to steer the tug in the opposite direction as the inertial forces that cause the sway, especially under braking.