For starters, Low voltage wiring is not much different from the higher voltage we use in buildings, but remember ohms law, this will produce much higher current levels, and resistance of a circuit can be a problem on long runs, which will cause bad voltage drop problems, never use a listed outdoor transformer, or circuits from one to feed indoors, or visa versa.
18awg seems way two small for this transformer, as it shows the smallest conductor to it as a 14awg. this transformer has two transformer cores, each core has two protected outputs, these are likely a auto reseting circuit breaker, at about 25-30 amps.
Three things to keep in mind when sizing the wire is, how many lamps can be on each circuit (300 watts total each circuit, 1200 total with this transformer), wire size, and voltage drop. I run a ring circuit sometimes to over come the voltage drop that leaves the lights at the end of the run looking dim, by running through the circuit alternating every other light, then back picking up the ones I left out, then back to the transformer making sure of the correct polarity this places each light at the same voltage drop in the circuit so they will all have the same brightness.
But as to your original question. First, in these applications polarity is not an issue since it is an AC circuit and a resistive load (incandescent lamps), but can be a factor in a ring circuit.
As to where to put the lonely wire? you have to have two conductors to make a circuit, one wire wont do it, so I would say you need to find the other wire that will complete the circuit and make sure one is attached to the common, and one is connected to one of the taps on that section of the transformer, always use the lowest tap voltage like the 12 volt one first, then check the voltage at about the middle of the whole circuit, then select to correct tap to bring the average voltage back to the 12 volts needed at the lights, if this is a single run you will have a higher voltage reading at the closest lights to the transformer and have lower reading the farther you get from the transformer.
Hope this helps:wink: