I just installed a tail tidy kit with LED lights. I ran into the same issue and found that i had signals crossed. I wired mine as follows.
From Harness I purchased=Red lead was ground and Brown lead was power. I had a spare blue wire that was not connected.
I bought my harness adapters from TST industries with there LED relay. I plugged both harness in to factory plugs and performed a tone test to find ground.
I did a voltage test on the other leads and that's how I found the Brown lead was power. All turn signals work as they should and with the relay I don't get the fast blink!!
If you have any questions please let me know.