Just to clarify, since I don't know if my experience is what you all are describing: this sounds kind of like what I hear if I start a yawn. Is the rumbling sound just for a second or can you make it indefinitely? And can you also make a short click or series of clicks?
I can get those sounds if I tense up some muscle(s) that you would also use to start a deliberate yawn. The clicks are easy to make, with less tension, and the rumble happens with more tension and it's only for about a second or so. Also I definitely hear the rumble during a yawn. Does that sound like what you mean or am I describing something completely different?