It will trigger a relay if you use the mute output to trigger a relay. You would do this by connecting terminal 86 of the relay (coil +) to ignition 12v and terminal 85 (coil -) to the ALP mute output with a diode for the reason in my last post. You can still use that same output for radio mute, you would just run a second wire to the radio mute with a diode.

So:
12v ignition -> relay terminal 86
ALP mute -> relay terminal 85

This will operate a relay, this is called a negative trigger. The relay coil is being triggered when the ALP provides ground.