Does this model have a mute indicator light?

No. There are audio messages (Female voice, saying 'Mute On'/'Mute Off') when you place yourself on mute and take yourself off mute. Also, while on mute, the device beeps softly at regular intervals, letting you know you're on mute. There is a red circle that lights up when you're in an actual call, but that has nothing to do with whether you're on mute or not.