Why do my brakelights go out when I turn on my.

You should also find improper operation when you turn on just the tail lights, and the turn signal. That is due to a broken ground wire. To verify that, if the right one doesn't work properly, for example, it will go out completely if you remove the LEFT bulbs. I can explain the reason for that, but for now, look at the wires to see if the one bolted to the body is broken or corroded. If you have trailer hitch wiring and someone used those blue Scotch-Lock connectors, they don't seal out water and are the first place to look for trouble.