Why did my headlights kill my car?
Get out your wiring diagram and start at the headlight connector and trace back to the battery.
Along the way see where the power to the ignition taps into the the system bact to the battery.
Just a while *** guess. The main splices, ammeter, or bulkhead connectors would be my bet for an intermitant complete electrical loss.
As to why..
Lets say you have a bad connection in the bulkhead connector on the main battery / alternator connectors. To just run the car the resistance is not too much and it runs ok. Now add the additional current of the headlights, the bad connection starts to heat up creating additional resistance to the bad connection. You hit the high beams, additional current now the connector heats up enough to brake the connection, (metal in the connector expands) now it sits for a few minutes and things cool off and the metal retracts and makes a connection enough to run the car.
Could the high beam switch caused the problem? I doubt it
Could the headlight switch caused it? Maybe for the lights, but why would it kill the engine????
Now maybe, just maybe, your battery is very low and your alternator is not charging enough and when the lights are on it can't keep up to the load and after a while the voltage is so low that the engine dies.
Does not fit your description of the failure but easy to check.