Where did that "suggestion" come from? I'm afraid I don't know anything about rattling Back Flow Preventers. But you have a good one, and good ones can be tested by someone with the proper test equipment.
If you google "back flow preventer testing in Sun City West" you'll see a slew of companies that can do it. But...
These days it seems plumbers want $300 just to show up, and the price goes up from there if they have to lift a finger. A good BFP (you have what's known as a vacuum breaker), suitable for a pool auto-filler, has gone up a lot in price, but is still about a hundred bucks.
Here's one similar to what I have, it's a good brand:
If you have any DIY in you, you might find replacing it is cheaper than even getting it tested. And if they find something wrong with it, you might pay double to have it replaced PLUS the charges for testing and a couple of house calls. There are also rebuild kits available, so you could fool around with one of those and a YouTube video about how to rebuild your model.
The image you post shows only the unit, not any of the plumbing. Can you take a shot of it further back? Is is connected with PVC, or iron pipe or copper? If it's PVC, the DIY replacement would actually be very easy.
So those are just some alternatives for you.
I've sent an email to my BFP guru buddy to see if he has any suggestions. So you might stand by for his response. When folks here point BFP questions to the resident BFP expert (me!) it's really only because I know a guy who has the answers! It was he that provided a lot of the info in our Further Reading article. It might take him a few days to respond to me...