OK. So this jibes with my instinct above as both simple and efficacious.
How do I do it?
I'm assuming I need a power supply, a dc low voltage converter, A relay switch as you say... Perhpas a resistor to bring the trigger out voltage down so it stays safely below 12v...
I would guess the input trigger signal goes to the relay switch, which I would further guess needs to be powered (hence the suggestion of the ac power supply and dc low voltage converter).
It strikes me as I type this that there should be a device like this in existence...
In my garden I have an AC wall wort that converts to low-voltage DC out and works from a brain that tells it over rj12 connection when to trigger. In this case, the trigger activates a solenoid irrigation valve.
Overall the garden controller is much more complicated, but similar in concept...
is there a device that already does this?