AFAIK = "as far as I know" i.e. I think this is the case, but I could be wrong ("BICBW").

Pull-down resistor: if you have a simple switch connecting the mute input to 12V, then you'll get 12V when you close the switch, but when the switch is open, you could get anything. So you put a large resistor (100K, say) between the input and 0V, which pulls the input down to 0V when the switch is open. Or, you can switch the input to 0V and have a pull-up resistor to supply 12V when the switch is open.

The alternative is to use the kind of switch (double-pole? double-throw? I can never remember) that selects either of two inputs, and provide 0V on one and 12V on t'other, with the "common" terminal connected to the players Mute input.