Yes, that's what I was thinking.
Put the + or red lead of the voltmeter on the + terminal of the battery, and put the - or black lead of the voltmeter on the + terminal of the siren. No need to connect volt meter to ground. Turn on the siren and make sure the wire isn't getting too warm. See what the volt meter reads.
I=V/R
7.5 ft of 10 gauge wire is .007 ohms.
So, for example suppose you read .28 volts, .28/.007=40 amps. In that case I would get a 50 or 60 amp circuit breaker. I'm going to be surprised if that siren draws that much and if 10 gauge wire gets hot. But I've been surprised before. If it has really high current and it is convenient for you to move the siren closer to the battery, that will help shorten the wire and that will handle higher current with less voltage drop.
It may be a good idea for you to run an equal gauge wire from the - terminal of the battery to the ground of the siren, so you don't rely on the ground provided through the engine block and the small ground straps between engine and truck body.
If the wire gets hot, I would consider the measurement and calculations just a rough estimate, and would probably be a good idea to go to bigger wire and re-do the test and calculation.
I suppose you could use a short piece (6 to 9 inches maybe) of fusible link wire at the battery + terminal instead of a circuit breaker or fuse. The fusible link wire should be 2 wire sizes smaller, which is 4 numbers because electric wire is just sold in even sizes. So if you have 10 gauge wire to the siren that means you would use 14 gauge fusible link wire. That is a wire with a special non-flammable insulation. Fusible link wire is supposed to burn up first, protecting the main wire. That is why you buy fusible link wire that is smaller (bigger number gauge) than the wire you're protecting.
Here's a resistance calculator for wires of various lengths and sizes:
https://www.cirris.com/learning-cent...lculator-table
Here's an example of the type of circuit breaker I was thinking about
:
https://www.wiringproducts.com/50-am...-parallel.html
Chart for figuring out the right wire size. This is for a max 2% voltage drop and your application is not sensitive, you may be able to fudge on this a little and just have a higher voltage drop and the siren will work fine.
http://info.waytekwire.com/blog/auto...e-gauge-guide/