My understanding now is that a neutral carries the unbalanced load in a separately derived system? However, since this is an auto Transformer There is simply a common and not a neutral.
Now you're confusing the neutral of a 120/240v 3-wire supply with the neutral of a 120v 2-wire supply. They are the same conductor, to be sure, but we're discussing them for different reasons.
Look at the drawing above. That's how two fixed auto-transformers would be wired. The bottom wire runs unbroken from source to load. Code specifies that auto-transformers be wired this way so the common, fed-through conductor is connected to the source's grounded conductor.
Since there are two, and they (hopefully) are wired thusly, the wire we're talking about already, or rather still is the neutral, or grounded conductor. By "grounded" we're referring to the neutral, white wire, as opposed to the hot, black (or red) conductor.
Now, none of this post has anything to do with grounding, which is the green (or bare) conductor.
If either of your transformers has isolated windings, like a conventional step-up or -down transformer, you have a separately-derived power source, defined by having no conductors connected to the primary or earth. Such a circuit should have one conductor grounded by being connected to earth by a grounding electrode conductor.
Note that this conductor has nothing to do with the source's grounded conductor, which is what we mean when we say neutral. The neutral is indeed grounded by being bonded to the system grounding electrode system via what we call the main bonding jumper, which is normally located in the enclosure housing the main service disconnect.
After the main, the neutral (grounded) conductor and the grounding conductor are not interchangeable, should never be interconnected again, and neither should be used in place of the other.
Is this a hard-wired installation, or a plugged-in bench-top experiment?