Where do look for a brake light problem if both fuses are OK and the lights all went out at once?

Lights Don't Work

Without doing a "hands on" troubleshooting of your vehicle, no one can tell you what defect is causing your problem. Therefore this answer will of necessity be of a generic nature.

Usually this type of problem is caused by what is called an "open circuit" condition.

Open circuits can be caused by several things, a few of which I can recall now:

• A disconnected connector [or splice] in the circuit.
• Corrosion or road film buildup on the contacts inside a connector.
• Corrosion in the metal "socket" the lamp [light bulb] is inserted into.
• A cut or broken wire in the circuit including the ground wire between the lamp socket and the grounded car body sheet metal.

In your case since all lights were lost at once, it suggests that the first and last items in the list above are the most likely cause of the failure.

The "proper fix" is for someone who knows what he or she is doing to troubleshoot the nonfunctional circuit, find and identify the problem, and properly repair it.