In reply to:

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isn't constant power 'low' voltage for the clock to remember the time n' stuff? or am i just going bananas...

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It's 12 volt, same as the main power. But it's a low-current supply (you don't want to be draining the battery all the time...). That shouldn't cause problems for the mute input, as that will draw virtually no current.

In short, it's okay AFAIK to connect your switch to the constant supply. You'll probably want a pull-down resistor, too - or a double-pole switch.