Headlights go off

You are correct that there is most likely a short to ground but the fact that it is so predictable sounds more like an open circuit. So, I suspect what is happening is there is a contact in either the switch, relay, fuse, or connector that when it gets hot, it separates causing an open circuit and the lights cut off and then it cools down and makes contact again and they come back on.

The way to find this is to hook up a meter on the circuit after the switch and monitor the voltage. Then when they switch off, we need to start testing these components to find where the power is. If there is no power after the switch, then we need to go before it and if you have 12 volts going into the switch then the switch is the issue.

https://www.2carpros.com/articles/how-to-check-wiring

https://www.2carpros.com/articles/how-to-use-a-voltmeter

Basically, when you are checking the voltage, you are supplying the ground through the meter. This means if you have power going into the switch but not out then the switch is opening up and not providing the path to ground which will be your issue.

I suspect the switch as this is the most common failure, but the same principal applies to the other components.

We don't have a wiring diagram for this vehicle as it is older, but it should be a simple two wire switch which is power in and out and the switch breaks the circuit for on and off.

Please let me know what you find or if the switch is different, can you get a picture of it, and we will figure out the next steps.

Thanks