It sounds like this "flat plain grey 3 wire set up" is a piece of cable intended for 120VAC household use, but used in the trailer for 12 VDC. Since the green wire is insulated, it's not the solid-conductor cable for built-in service; it's likely flexible extension cord. It is really unlikely to be larger than 12 gage, and may only be 14 gage, which is marginal for any significant load.
I assume that this cable does not connect to the tow vehicle (and thus is unrelated to the wiring which Al has described), it is not polarized (no indication of which wire is which because the two main conductors are identical), and the green-insulated wire is intended for use as the ground, which does not apply to this DC trailer application. I would consider replacing it.
Also, judging from the test, the negative side of the battery is grounded, which is apparently not normal practice in travel trailers.
1979 Boler B1700RGH, pulled by 2004 Toyota Sienna LE 2WD
Information is good. Lack of information is not so good, but misinformation is much worse. Check facts, and apply common sense liberally.
STATUS: No longer active in forum.