G'day Peter,
No, that short of loss of power would be involved with the power from the Battery itself.
Loose battery terminal, poor connection at the Starter Motor Solenoid.
The power to the headlight switch is directly from the main power supply, whereas the Ignition power is via the ignition switch.
Actually, you could have a faulty Ignition Switch if the power take-off to the headlights is from the battery terminal of the Ignition switch.
I cannot recall what my own '60 had as the wiring, as it was converted to RHD, and therefore not original.
We depart for the Renmark sojourn on the 16th March, and pulling into Renmark on the Wednesday.
Bruce.