[AZKen]

Headlight switch has a thermal overload feature. Those contacts are corroded. If it's a new switch, then some Chinese guy screwed up the assembly. The overload metal contacts are cooling off and resetting. You may have a good switch and thermal overload contacts and your problem is that something else is overloading. Bad relay, bad dimmer switch, wiring messed up/small short, bad filament in a headlight, headlight connector.

The brake light issue, on one side, should be easy to trace. It's not beyond the realm of possibilities that the two are related.