I was randomly seeing the notice to check trailer wiring on my 2020 LT when towing travel trailer, but trailer brakes and lights were working normally. Dealership found stored code C1114 (no MIL) and gave me this TSB. I bought the Pollak 12-706 trailer plug from Amazon and have not seen notice since, despite the Pollak plug being thin plastic. Good luck.
TSB 21-NA-155, Date: June 2022
https://static.nhtsa.gov/odi/tsbs/2022/MC-10214860-0001.pdf
Subject: Information on Check Trailer Wiring Message and/or Service Trailer Brake Displayed on Driver Information Center (DIC) - DTC C1114 Set
Engineering has recommended the use of
Pollak Heavy Duty 7-Way (Trailer Side) Connector Plugs. Pollak is the OEM
manufacturer of the truck's 7-way connector socket; and by using a Pollak Heavy Duty 7-Way (Trailer Side) Connector Plug, this will ensure proper fit when the twoc onnectors are mated... (example 12-706, 12-702).