It's time to get methodical with your voltmeter. Hook up the light switch out of the dash panel so you can access each terminal and wire. Make a drawing of the wires coming out of the switch using the 2 PDF diagrams I downloaded from Chilton. Use the diagram colors to label each wire on your headlight switch.
In general terms the 12 volts enters the switch, goes through the switch, and comes out of the switch. Then it goes along that colored wire, through fuses (maybe) and to each bulb socket. Then it goes through the bulb filament and to a ground return.
For the first quick test set up your voltmeter to monitor the voltage on the headlight output wire at the switch. You can use a 12 volt testlight or small bulb instead of a voltmeter.
When the headlights go out (by themselves) check for 12 volts coming out from the switch. Voltage means the switch is getting power and feeding it toward the headlights. But no voltage means the switch is becoming open, or the main power feed into the swich is disappearing.
This type of testing works for the taillight circuit or the instrument lamps circuit too. Once you know the headlight switch is working you can move your tester out to each socket.
Beware ... sometimes an open or poor ground at one of the sockets will allow a small amount of curent to back feed into another socket. A voltmeter will show that as a voltage, but a test light will be a more accurate test.
Be methodical, draw any kind of diagram to keep track. You will get there.