Probably Flasher
emergency blinker
When your tail lights are out you can simply replace them. If they continue to blow, you may have an electrical problem.
It has been my experience that when the blinker comes on but the lights don't blink there is one or more bulbs burned out. If that is not the case check the flasher.
A simple first step would be to check the fuses to these lights, then go from there.
The emergency blinker switch on a 2008 Prius is located on the dashboard, typically near the center console, above the radio. It is a red triangle button that activates the hazard lights, allowing all turn signal lights to flash simultaneously to alert other drivers of an emergency situation. To use it, simply press the button, and to turn it off, press the button again. If the switch is not functioning, it may need to be inspected or replaced by a professional.
The next thing to check is the switch that activates the brake lights. It is probably on the master cylinder.
The tail lights are on a separate wiring than the blinker/brake lights. Look for a blown fuse or a broken/loose wire.
cheack the wireing
your problem could be in the switch its self. unfortunetly they are expensive to replace, i had to actually wire a switch direct to the blinker system.
Bad earth connection at light cluster?
Cycle the emergency 4-way flasher switch on and off a few times. If it doesn't clear up you may have a faulty signal switch.
try replacing the flasher. there should be two, one for flashers and one for turn signals