Wiring Harness for Towing a 2012 Prius v

Have you looked in your owner's manual? I vaguely remember seeing some details about towing the v. I think there was a warning about towing - maybe that you're NOT supposed to tow it backwards (with only the front wheels on the ground), or else the hybrid system could be damaged? Even if the manual doesn't list info about the wiring connections, definitely look it over to be sure you're towing correctly.
If you don't find what you're looking for here, check at your local UHaul shop. They stock a wide variety of wiring harness and trailer accessories for general towing, so I'd bet they have info (or maybe specific parts) for towing a vehicle also.
hope this helps,
Andy

 

I believe the OP stated the Prius would be towed on a dolly, so no wheels would be on the ground and no damage to the Prius.

 

I tow my Prius with a dolly and connect my dolly lights to my motorhome for turning and brake lights.