Thank you for all of the details about troubleshooting the Curt T-Connector # C56254 on your 2013 Hyundai Accent.
Since you said the ground is secured to a clean, bare-metal surface and all of your other wiring looks to be in order it is very possible that the issue is actually on your trailer, but I recommend using a circuit tester # PTW2979 to see whether the power is getting to your 4-Way connector or not. If the tester works fine then the problem is on your trailer, but if it isn't... view full answer...
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