2005 Dodge Durango trailer tail lights

Asked before and answered by someone who did not read the entire question:

I have a dealer installed tow package including taillight wiring.
I have tested at the rear of the vehicle and the trailer lights.
1. All bulbs and wiring check OK on trailer.
2. I have turn signals and brake lights ONLY if I do not have the tail lights on.
3. What do I need to check or replace so the turn signals will flash when the tail lights are on?