It's NOT the device. I'm getting these readings at the panel with the wiring disconnected at the base of the mast. And it happens regardless of which breaker I test. SOMEWHERE there is something grounding the system.
Are you measuring across the breaker, + input terminal to + output terminal, and getting 0V or are you measuring + terminal, input or output to ground, (return) and getting 0 v.
If you are measuring + Vdc in to breaker to + Vdc out of the breaker and when open read 12vdc and 0vdc when closed then your breaker is fine nothing is hokey. You just put a wire across a voltage drop when open, i.e. You have 12 volts on the battery side, and an open on the load side which your meter will read as somewhere near 0 v so the meter will read around 12 volts. When you close the breaker you now have equal potential from the battery source to the end of the wire, by placing both leads any where on this wire you should read 0 volts, as in no difference in potential in the wire, when you open the breaker this reverses the setup and you have 12vdc on the battery side and nothing on the load side, resulting in a reading of 12vdc difference. Your "phantom ground" may be provided by your test set up since you removed the streaming light as a load it is now floating with nothing to reference it, when you use your meter, while meter due have high impeadence to avoid affecting circuits it is not a true open, so it does provide a path for current resulting in your voltage display when the circuit is open, and 9 once you close the breaker and the entire run is at the same potential.
That said, with out pictures of what you are reading and how it is hard to tell, assuming it is a fault in the circuit, low voltage and a load usually is the result of excessive resistance, so check the usual suspects, check contacts and inspect them, greenish tint for copper, white or grey ashy for aluminium indicate corrosion.
Also check their condition, do they look good and uniform are the wires damaged going into the connection? do they have enough play so not to be over stressed? Does the insulation cover the entire wire? or does it gap right at the end? If all these are good, then you need to inspect the entire wire run is the insulation in good condition and free of abrasion and cracking? Any tight bends, a tight bend is one that is less than 5 times the diameter is the general rule. Look for errant screws that could have abraded the wire and fix the issue and the wire, i.e repair if necessary and move the wire away from the screw and secure it so it cannot happen again.