Here's an analogy: you're trying to suspend a load with a rope. You can't buy the correct rope until you know what the load weighs. Similarly, here, you can't buy the correct relay until you know what current and voltage the relay must be rated for. We know the voltage -- it's the nominal automotive 12 volts. The thing we need to know is the current these sirens require when operating. This is usually specified on a label of a device, but if there isn't one present, you have to measure it with an ammeter. This is conceptually pretty simple
to do, but it's got some practical problems: if the siren draws more current than your ammeter's maximum full scale current, you'll blow a fuse in the ammeter (or damage the ammeter if it doesn't have a fuse). In some digital multimeters, this can mean replacing the fuse, which can cost $5 to $15 for a new fuse. The best tool is a clamp-on ammeter that can measure DC current because you don't have to worry about blowing a fuse. But you're unlikely to have one; however, you might have a friend or coworker that does. If you were near by, I'd do it for you because it only takes a couple of seconds. I'd use
this meter because I have one handy.
Once you know the current that each of the sirens draws when operating, then you're ready to proceed with the rest of the design necessary to have a proper and safe installation. If you can't measure the current spec, then you should try to call the manufacturer and get them to tell you. Failing that, you could go to a service place (like an auto repair place, stereo shop, etc.) and pay them to measure the current for you.
I'd imagine that these things are probably on the order of 50 W to 100 W of power maximum. That means the current will be approximately 5 to 10 A (I used an efficiency of 0.8). But you want to measure it and know rather than guess and run the risk of guessing wrong and making an installation mistake. An installation mistake runs the risk of causing a fire, so it's clear you want to do things right.
