Do you have a garage door opener? The one I have (Craftman Security+) has three buttons on it to open three different doors. Just go online and buy a garage door receiver. I think they run about 50 dollars US. These receivers provide a contact closure for the length of time you hold down the button on your garage door opener and they operate on 12 volts. Wire the receiver to provide a signal to the acc. power input of your Rio. When you pushed the button on the remote it would then put your Rio in standby. Would this work?
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