2012 Tail, license and rear turn signal lights not working-Fuse blowing

I suggest that you will need to subscribe to techinfo.toyota.com so that you have access to the electrical wiring diagram for your model year, and can see how the circuit is wired, as well as the color of the wires involved. You'll also need a digital multimeter so that you can measure resistance to body ground.

When you are equipped with that information and the meter, then you can measure resistance from the 10A TAIL fuse socket to ground, on the side of the fuse socket which leads to the lights. That resistance will probably be close to 0 ohms since the fuse is blowing. Then the task will be to identify and disconnect the various connectors that are in the path from the fuse box to the rear of the car, one at a time, continuing to measure resistance to ground. That will help you to figure out where the short is.

Suppose you start with the wiring harness connector closest to the fuse box. If you disconnect that and find the resistance becomes infinity, then you know the problem is not between the fuse box and that connector. Then reconnect, and find the next connector. Repeat until the resistance remains 0 ohms. At that point you will know the fault is between that connector and the prior connector. Then you'll need to examine the wiring to find the fault.

You'll need to remove the hatch lining trim to access the wiring to the tail lights and the license plate lights. That 10A TAIL fuse also powers the side marker lights in the headlight assemblies, so that is yet another set of wiring that potentially could be causing the short.

This is not going to be an easy task if you do not have prior experience troubleshooting electrical shorts, interpreting the schematic wiring diagrams, or using a multimeter.