Ah, yeah. Not exactly what you were hoping for, but there it is.

I suppose if you can find a bluetooth adapter that has a "paired LED", then maybe use the wire from the LED for the purpose?

EDIT: Or maybe just tape a photoresistor over such an LED, to detect when it is illuminated, and wire one lead of the photoresistor to the MUTE input, and the other lead to either ground(earth) or +5/+12V at the empeg?

This avoids having to attempt disassembly of the BT adapter.