Want to catch him, set up a webcam and hide it. Video evidence, indisputable. There's software you can get that only records when the camera detects motion.
How much is this actually costing you though? I don't know what the cost per gallon is where you live. If it's not that much, I'd just cut my losses. Last thing you want to do is start a war with your neighbours. That can turn into a bigger headache than some lost water. If it comes to a couple extra bucks on your bill, bit the bullet and shut the water off. Once he realizes you've caught on, he likely won't try to do it again.
If it's a lot of money, then by all means demand they pay for it. However, it's difficult to prove that it was him each and every time. Keep a careful record of your own water usage. Your meter should have a readout on it. Catch him in the act a bunch of times, record how much water they used, then present them or the police with the evidence. If it becomes a civil matter, those logs will be your best friend.
Before you do anything, check and triple check for any leaks. Slow drips can add up fast.