When I pulled into the garage the other day, I noticed that my antenna did not go down when I turned off the radio. No activity at all when the radio is switched on or off, no noise from the motor. The red wire running to the antenna has 12V constantly. Unless something is telling it to stay up, it should go down, correct?

I removed the antenna to investigate further. No action when I apply power to the terminals at the relay. I can unplug the relay from the antennna and apply power directly and the motor works as it should. Goes up and down with reversing power to the terminals.

What can I check next?

If you haven't already, check the relay.

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How do I go about checking the relay? I am guessing that you mean the plastic box that plugs in to the motor?