This is strange! I think the sensor relays the MUTE instruction to the MCL2AV via the data stream, and your IR is working so the mute should be as well. I did once have to take apart an MCL2 sensor to fix a faulty mute switch – from memory it simply wasn’t making the correct electrical contact when I pressed the button. So a faulty switch is not unheard off, but it seems a strange co-incidence that neither of yours work!
I think your assumption about the Mute function being through the data stream is true for the MCL2AV. On the diagram for the IR eye /Transreceiver in the service manual the yellow wire is connected to a output called mute on the chip. (note the servicemanual is for a type 2021 and the 2 I have is type 2047, so there might be differences)
However on the MCL2AV it seems like it is connected back to the grey wire which is is also an output of some kind on the IR board chip.
On the MCL2A diagram the yellow wire is conencted directly to the ciruit with the mute relay for the speaker, so it might be used differently on that unit.