The 10 year old yapster's microphone finally died.  It was strangely a broken ground to the microphone, somewhere in the cable & probably near the knot.  Normally the thinner wire breaks.

Soldered into the speaker ground.  Didn't do a good job insulating the solder joints but it worked.

The microphone arm is held on by a self tapper from the inside.  Tightening the self tapper increases the friction.  There's no spring or knurled surface.  For animals wishing to add a microphone to normal headphones, it would entail something like this.

Using a directional microphone didn't work.  It was too sensitive to wind.  It has to be omnidirectional.