it really is of no consequence to me, so i will only address this
"Iv had experience with all three. with the first two kinds your right on. the third non swiveling non stearing kind you drive on like normal then a harness fits over each front tire and gets tightened down so the wheels cant move at all on the dolly. but the car stearing is unlocked so the vehicle pivots instead of the dolly. If the vehicles stearing is left locked when you make a sharp turn you would be dragging the dolly axle side ways.:"
if the wheels are strapped down to the dolley, and the dolley does not pivot in the center, or have a tie rod steering system built into the dolley, there is no way on earth for the cars steering to allow the unit to make a corner! it cannot happen as described
the cars steering will not allow the car to bend around the corner,
the only way for this to possibly work, would be to make a very complex table system that not only would have two tables, one for each wheel but they both would have to swivel, and they would both have to traverse forward and backward on the dolly chassis.
when a car goes around a corner the inside steer tire only goes a very short distance, while the outer must travel a much larger distance. if you strap the wheels down to a common line (the cradles are inline with one another) this would preclude either wheel from traveling further than the other, they would have to travel the same distance no matter what because they are strapped down and the car does not bend in the middle.
you can try this if you like to prove my point, load the car on the dolley
turn the steering all the way to either the right or the left and lock it down there, then strap it down tight, and drive off straight. you will find the car will go just fine following the tow vehicle just fine. now make a left turn and it will turn just fine.
if you don't want to try that, just cut out a little cardboard T and put a model car on it, and then turn the end of the T, and see where the tires go. allowing the tires to steer will not make a difference, the wheels will still move off the T, one forward and one backward, which depends on direction of the turn.
this whole leave the key on or unlock the steering is a throwback to the towbar days when you had to do so if all wheels are going to be on the ground.
anyway, this is all a sidebar i realize
as for charging the towed vehicle off the tow vehicle, you won't overcharge the towed unit, if anything you will be undercharging it, or at best maintaining the charge, because of the voltage drop in the cord from the tow unit to the towed unit.
many of the motorhomes use a lower set point regulator because the unit is going to be on the road over longer distances, not city start and stop generally, so... it is not uncommon to see a setpoint of 13.8 or so at the alternator, drop another volt in transmission via a 12gauge wire and you will be just about what it takes to keep from taking anything from the towed vehicle battery, not enough to do any real charging, but maybe enough to run the lights.
you would still need some means of stop, turn and hazard to the rear of the tow vehicle anyway, so i would think maybe instead of worrying about powering the tail lights off the towed vehicle battery, simply disconnect it if necessary and run a separate set of remote magnetic mount lights from the tow vehicle to the mount at the rear of the vehicle in tow.
sorry for the argument,
i just don't want any part of propagating something that might end up getting someone hurt down the road. i am not saying it is the case here, but there might be others that read this and think it correct to unlock the steering when there is clear evidence to the contrary.
if that makes sense?