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Check the connections again.
First, trace the full length of the wiring. Make sure there are no cuts, bruises, strains, etc.
Second, remove one connector or disconnect it. With a clean dry brush, scrub the connector on both sides of the connection, at least 20 seconds. Then with a clean dry lint-free rag cloth, wipe the connectors on both sides until the metal shines, and re-connect firmly - then on to the next connector/connection, and treat it similarly.
Third, once those are all done, cleaned and checked that way, you may power On the Garmin and the radar transponder, and see if they work together.
Let me know more, if that does not sure it.
(If that does cure the problem, then please rate my answer, or at least, let me know, please. Thanks!)