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I am trying to decide if I can run the relay directly from the 12V trigger
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Not really common practice to do so.
When you have found the suitable relay that can handle the 15amps and voltage >~125volts you'll be switching, then determine the coil current required from its coil resistance spec. You'll find that a relay of this size usually requires being driven from a transistor or another smaller relay. Don't forget to back bias the coils with diodes.
You can certainly use an internal 12volts found in the amplifier to drive these parts.
A 12volt trigger would generally be able to source about 80 ma. That spec would be available with the equipment you'll use to send the trigger from...
brucek