Can I run my audio mixer off the battery powering my amplifier?
Likely yes. 16V is the next size up capacitor rating, and most component have a tolerance for a single volt. Likely there is a regulator that drops the voltage inside anyway, and an inverter to provide a negative rail too. You could Crack it open to verify, but just to be safe put a standard 1n4001 diode in series with the input voltage, to bring it down about 0.7V. The same applies to undervolting it, slightly less than 12v is fine too.