2005 Dodge Durango Trailer lights

Dealer installed tow package in 2005. I have turn and tail lights but not both at the same time. From mileage, you see I use the vehicle infrequently, and although I always checked to see I had turn, I only recently checked with tail lights on, so I don't know if dealer left something out, or I need to replace something that quit working. Please advise. Thanks

I thought I stated this, but yes I checked at the plug at the rear of the vehicle. I show current with directional signal - 12v then 0, 12v then 0 as the blinkers blink on and off. I have 12v to tail light connector, but it does not alternate 12v then 0 as the blinkers flash.