Yes, the Upgraded Circuit Protected Tail Light Converter Hardwire Kit w/ 4-Pole Connector and Circuit Tester
# 119178KIT is the correct wiring harness for your 2013 Toyota Faris.
Since everything tested good at the 4-pin adapter, it sounds like the issue is on the trailer itself. I suggest checking all your ground connections to make sure one hasn't disconnected or become corroded. A bad ground can cause any number of weird things to happen, and this definitely sounds like what is going... view full answer...