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It's possible that's all that is needed. However the thing to know is whether or not the plug on the end of that is providing 12v or 5v. Many cigarette lighter adapters have circuitry inside that is converting 12v to 5v. Most electronics run on 5v, not 12. I'd use a meter to check the output.

 

You can use that power or the power for your radio - on the battery side of the harness, the power is always on. I would not use tape. I would do it right with solder and shrink tubing or splice in with a crimp connector.