I had this annoying rattle for quite a while, which was more pronounced when the engine fully warmed up. It was clearly audible when sitting in the car at a red light, idling. It got worse as time went by and I could hear it sometimes even with a cold engine. It sounded like this.
Then I read that the culprit is the SSV actuator arm, which rattles against the stop it rests on, and the solution is to wrap this stop with a hose.

To avoid a problem due to the heat, I used silicone hose. You need very little of it of course, so I ended up with a lot of leftover - but at least I have plenty of spare if the wrap ever needs replacing.
It is rather difficult to access the stop, and I definitely wanted to avoid having to remove everything in the way to get at it. I was able to get this done from above, by hot gluing the small piece of silicone hose perpendicularly onto a wooden rod and forcing its end onto the stop with that. The hot glue barely held the hose to the rod so it came off easily, then I used my hand to push it all the way onto the stop. Lost some skin due to the tight space, but finally succeeded.
This is how it looks now:



This eliminated the noise for me, and it sounds like this now.
I drove about 1000 miles since the repair and checked how the silicone hose holds up. So far so good, there is no sign of damage or any other problem. Hopefully it stays that way.

 

You explained it very clearly. It's an excellent solution to resolve this noise, which is quite annoying.

But does anyone know exactly why it happens? Does a particular part wear out after a few years? This noise is quite common in RX8s.

I was once told it was because it was getting dirty with carbonized oil, so I took out the SSV (not an easy job) and it was very dirty. I cleaned it and it was as good as new, but after a couple of days the annoying noise returned. Another mechanic told me the problem was a rubber seal inside the valve seat. I'll check this last one one of these days because I have the engine disassembled right now, so I'll take it off again to check.

 

From what I read, this noise comes with age. Some bushing wears out a little and it's a bit loose, so the actuator arm gets a little more play and starts to rattle.