The fact that the brake lights on your trailer are staying on all the time indicates a possible short somewhere in the vehicle or trailer wiring. Although it's pretty unlikely with the connector being new, I recommend first checking the connector at the rear of the vehicle for any dirt or debris that might be causing a short.
If the connector looks fine, I recommend moving to the vehicle wiring harness.
The Tekonsha ZCI Circuit Protected Vehicle Wiring Harness # 119250KIT is particularly... view full answer...