I need help with a relay/coil

Im a bit confused when it comes to choosing a relay/coil. Im not very wordy with the terms so please excuse me.

I'm trying to remote swtich an inverter using my negative pulsed output from my alarm. My inverter came prepared for remote switching. It has three wires (1)+12v, (2) Ground  and (3) Open

When Wire 3 is grounded (Wire 2 makes contact with Wire 3) the unit switches on, and when theres no  ground it remains off. 

What I need is a relay/coil that when I pulse it with the negative output from my alarm wire 2 and 3 have continuity, and remain on until I pulse it again. My alarm does not have a latched output otherwise it be much simpler to just bypass it with a simple setup.   I don't know what I need, Im not sure if what I need is a relay or a coil or even both.

Please let me know what setup I should choose. Thanks so much....