Electronic – How to (optimally) connect Elk-924 (high sensitivity relay board ) to DSC PGM output (sinks to ground)

This sounds like a very specific question, but I think it boils to a generic one — not at all specific to this equipment. But it will take a bit of backstory to get there.

My background, btw, is software. Electronics is a new and recent hobby.

First the equipment:

http://www.elkproducts.com/product-catalog/elk-924-sensitive-relay

(Apologies, can't add picture due to insufficient reputation… you'll have to see the PDF.)

This relay board is powered by 12v and is triggered by what they call a 'highly sensitive' input trigger (T- and T+) that requires very little amperage.

• Operating Voltage:12 or 24 Volts D.C.
• Trigger Current: 1.2 mA @ 12 Volts D.C.
• Trigger Voltage: 5 to 24 Volts D.C.

The second is a DSC PC1864 board. This board has an AUX (12v) output along with several "PGM" outputs that basically sinks the terminal to ground under certain programmable conditions.

My primary goal is to close the relay under a certain PGM condition. My secondary goal is to power the relay through the same power source that I'm switching. Why? The DSC board has limited AUX power capacity and there's no reason to power the relay from the board if I don't have to. 60ma is almost 10% of the AUX's capacity, and there are other devices already on there.

The power source I am switching is to a camera, so let's call that CAM. It has its own 12v power transformer, not at all associated with the DSC board.

So this is what I did:

I connected the Elk's POS/NEG terminals to CAM +/-. I also connected CAM + (and camera) to the relays, the camera directly to CAM -.

I then connected the T- terminal to the DSC's PGM terminal. I found the camera stayed on all the time, measured voltages, and quickly realized — OH — I'm dealing with relative voltages. The T- isn't isolated from the POS/NEG source. Negative on each board has relative voltages, of course, and not a common ground. (right?)

So I connected the DSC's AUX +/- to the Elk's POS/NEG, and T- to the PGM terminal, and it works perfectly.

Question:

If I still wanted to achieve my secondary goal of not powering the relay from the DSC panel, and only connecting the trigger (T-) to the DSC panel — how could I accomplish this with minimal fuss? (I mean, obviously I could get another smaller relay powered by DSC's AUX+/PGM-, which closes CAM+/T-, but that's silly.) Is this a job for an opto-isolator?

And how do I properly size the component?

Thank you!