They don't turn the wrong way. They always want to go straight.
That wasn't the problem the OP had. He said...
So I posted previously about my tow bar. Went to tow it today and my tires were not tracking. When I turn they turn the opposite way and don’t straighten back out. Any thoughts?
Many of you may know this, and many may not care, but for those who are interested in how caster works like this...
With caster in either direction (positive or negative) turning the steering will tend to push one front tire down and lift the other up. The one that's being pushed down needs to lift the front end of the vehicle, so the weight of the vehicle tends to want to push the tires back to neutral. That's why caster gives you a self-centering feel and more caster will accentuate that.
When flat-towing, the towed vehicle basically acts like a single axle trailer, with the rear axle of the towed vehicle acting like the trailer axle. The front axle is mostly along for the ride, getting slid from side to side. When you are driving forward and turn to the right, that slides the front axle to the right. But when you are backing up and trying to get the "trailer" to turn to the LEFT you start the turn by turning the trucks wheels to the right, which pushes the front end of the "trailer" to the right. So a forward right turn and a reverse left turn both make the towed vehicle's front axle slide to the right.
If the towed vehicle has positive caster, that means the pivot axis for the steering is tilted back, and as the axis project down it projects forward. That means that the contact point of the tire on the ground is behind the pivot axis. If the front end is slid to the right there's a force to the left against the bottom of the front tires. Since that force is behind the pivot axis it turns the steering to the right.
So whether you are in a forward turn to the right or a reverse turn to the left, either way the towed vehicle's steering turns to the right. If you are going forward this is what you want and it settles with the front tires pointing the right way for them to roll rather than slide. But if you are backing up it never settles out, so it just turns the steering to full right lock as you try to back around a left turn.
Negative caster means that the tire contact point will be in front of the pivot axis. So now sliding the front axle to the right pushes the steering to the left. So now you go to opposite lock when going forward and it settles out nicely when backing up.
No caster means that the contact point is right on the pivot axis. Now there's no compelling force trying to turn the steering in either direction. There's also no self-centering force. So the effects on the steering angle can't really be predicted. But that predicts that the tires won't stay pointed in the correct direction, at least not consistently.