2006 883 custom, all lights work except for rear running lights all turn signals work. Lamps in the back are single filament

 

Unless changed, the rear turn signals are only turn signals and not running lights. That is why they have a single element bulb. The rear running light is the Tail light on the fender. That tail light also has a double element bulb and serves as a brake light.
The front turn signals have a double element bulb and work as running lights & turn signals.

 

Start by checking your brake light, which should come on when you press either front ot rear levers. It it works the tail lamp bulb has probably blown the running light filament, so replace. If the brake light doesn't work, fit a new bulb and go from there. Let us know what you find.