For most central vacuums I'm familiar with, the signaling is done using 12V AC, though that's probably not universal (though oddly enough, the peak voltage would be around 16.9V--fairly close to what you measured--are you sure you weren't measuring peak voltage instead?) Complete the contacts at any point (each port is in parallel) and the vacuum cleaner turns on.
Now here's the thing: by shorting out the contacts, you should have next to no voltage difference between the two contacts at the vacuum cleaner! If you put in a 12V AC NC (normally closed) relay (I'm assuming it's AC, but check your measurement again, and the ratings of the relay--they can often accept higher than their nominal value, and sometimes work on both AC and DC), you might put enough current through it to turn on the vacuum cleaner!
If you're familiar with microcontrollers, you might have better luck with a Hall Effect sensor on the cord going to the central vacuum cleaner--you'd be able to determine when (significant) current was being drawn by the vacuum. I don't know if anybody makes a simple adjustable current detecting relay, but that'd be ideal.