Combining trailer tail lamp and turn signal onto one wire
I am looking to attach a light to my tow vehicle that will be powered when towing via a 12 V wire.


I wouldn't tow via a 12 V wire. But I assume you just got your word order mixed up.







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. Car circuit.

In a car the light switch provides a path to ground when in the off position. 


When lights are switched on current flows through the lamp from left to right.
If the turn signal is switched on it puts 12 V on both sides of the lamp so it turns off. It will blink in anti-phase with the lights on the car. (This may be a problem for the guy behind.)
If lights are off and the turn signal given the lamp will blink in unison with the vehicle.








simulate this circuit

Figure 2. An additional relay is required to have the same effect on a single wire feeding the trailer.