How to wire a 12V remote switch?

I really feel like I should be able to do this, but it’s not working, so here goes. I have two wires connected to a DC power source such that there is a ~7V difference between them; I want to be able to connect these wires with a wireless switch so that I can open and close the circuit.

I bought this switch; it has 5 wires, the antenna, a 12V in, a 12V out, and 2 grounds (both grounds soldered to the same equipotential surface, so I guess the redundancy is just to reduce resistance).

I presumed that I could attach the 12V in wire to the + wire, the 12V out to the – wire, and the grounds to the electrical housing, but this does not allow any current to pass through; nor does switching the positions of the wires, or (for what it’s worth) attaching the grounds to different surfaces.

It occurred to me that all 12V might be required to flip the relay, but when I rigged up some impromptu 12V batteries from a bunch of AAs, I still couldn’t get current to flow.

Does anyone know what I’m doing wrong here, or is the switch defective? Is it even possible to switch a 7V load with a relay rated for 12? Am I somehow supposed to be using an external power source (although I can’t imagine why that would be necessary, or how I could with the five given wires)?