Also, see How to use code fences for a way to post code in a way that is readable on the forum.
The syntax is NOT correct.
On what event on Item Echo_Living_Room_BluetoothMAC do you want to trigger the Rule? When this Item changes? When it changes to a specific value? When it is updated? See the second link for all the possible Rule triggers.
Does the Alexa binding somehow see when your phone enables BT and change this Item accordingly? Or are you using some other binding to detect your phone?