Rear Tail lignts and running lights out on my 2007

Did you check to see if the lights were in fact out?

 

You can find the electrical wiring diagram as well as repair manual info at techinfo.toyota.com

The 10A TAIL fuse provides power to the front side marker lamps, the rear taillights, and the license plate lights. Since you say that the license plate lights work, that would be evidence that the TAIL fuse is OK.

What do you mean by "running" lights?

I suggest that you trace the brown ground wire on both taillights, which go to a common point. That point probably has a loose or broken connection to the body.

 

Mine just went out too - thanks for the tip on the brown ground wire, I will start there.

 

While looking for the wire I pulled both of the sockets out with the bulb still in, said the magic word and put them back into the fitting and they came on, one at a time.

I see lights out all the time in Prius cars and lost my head lights at 45K. A bit frustrating.