Trailer tail lights usually have 2 different circuits routed to them; stop/turn and then the running (tail) lights. Since your turn light functions are working but the tail lights aren't that just means you need to troubleshoot that specific circuit.
Problems with a lighting circuit can be located on the tow vehicle or the trailer so you can determine which end to troubleshoot by testing the running (tail) light circuit on your vehicle trailer wiring connector with a circuit tester like... view full answer...
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