Very hard to describe but it sounds like a metallic "thunk", almost like flexing the side or top of an empty paint can, or the sound one of those vacuum seal caps on a bottle makes when you open it, but larger, and it has a kind of "springy" sound or slight reverb to it.

It sounds like it is coming from the intake manifold/throttle body area in the center of the rear of the engine between the firewall and the engine.

It seems to happen mostly when the engine is at operating temp and it is hot outside. It happens when the engine RPMs are going down just as it gets to idle RPM. This can happen when coming to a stop and the RPMs drop to idle or I can make it happen by putting the car in park or neutral and raising the RPM to one thousand, holding it for a couple of seconds and then letting it drop to idle. (Raising the RPM to 1,000 then letting it drop doesn't always make the sound happen.)

It does not appear to be brake related as it can be made to happen in park or neutral with no brake applied. I was thinking maybe vacuum related, but what could it be?

 

You're either going to need to take a video or atleast narrow it down by simply listening closer to where it's coming from.

 

EX 2.2s had a vacuum controlled engine mount, or something to that effect, on the firewall side. I think it had to do with comfort aka NVH. You may want to check you vacuum lines leading back that way.

 

I had started suspecting the rear motor mount or maybe the solenoid. I know the rear mount is broken; scheduled to replace on Monday. I had already replaced the front and side mounts but the rear was just too much of a hassle to deal with myself.

If replacing the mount solves it, great. If not, I'll be back...