Since this is before rear brake lights were required by law (?), this is a somewhat murky subject.
And some Villiers powered beasties had near minimal electrics, so brake lights required quite some cobbling (by owners) to actually give them such luxuries.
What make of electrics does your bike have - Miller ?
And does it have a battery ?
What does the parts list for your bike show - anything ?
The period wiring diagrams sometimes show dotted lines for the brake switch wiring.
And the rear lamp may need some upgrading to have a brake light function.
This is the style of switch you sometime see on this era of bikes (this one a replica)
It usually sits on a little metal plate, and anchored by any conveniently located bolt nearby.
The spring attaches to the brake rod, usually by a little clamp
Other brake light switches are available, quite a variety in fact, its just a matter of obtaining something and figuring out where to attach it so it reliably lights up and retracts.
I'll find a pic of one on a bike, although it may not suit your setup.
Rear lamps for bicycles, with LED technology possibly can be adapted - they use battery power, which can be conveniently switched on/off for more limited road use. And require no vehicle electrics, just a suitable switch.
Hopethishelps.