Options to achieve this include using a light bar or wiring into the towed vehicle's wiring system.
The easiest, though not the most visually appealing, option is to attach a magnetic or strap-on light bar to the rear of the towed vehicle. The wiring routes forward to a plug and taps into the motorhome's wiring system near the hitch.
Light bar kits do not require the owner to tap into the towed vehicle's wiring system. This can be important if the towed vehicle is equipped with an antilock braking system (ABS), since most vehicle manufacturers do not like the brake light wiring to be modified.
Wiring into the towed vehicle's wiring system
If you are going to use the towed vehicle wiring, the most practical thing to do is to purchase a light wiring kit from a tow bar manufacturer or an RV component supplier.
Do-it-yourselfers can procure individual components and tackle the project themselves. The most significant component is a diode that is installed in the wiring to prevent current from going "back" to the turn signal switch.
If in doubt about diodes and circuits, seek the advice of an RV service technician or automotive wiring specialist.