I have personally experienced a bad battery cable itself. This was a non-OEM with the molded insulation going right up into the lead terminal. Inside, the strands of copper had become disconnected from the terminal. The tell-tale sign of the root cause was that if you turned the headlights on, then wiggled the cable there, the lights would intermittently blink on and off.
To rule this out, when the power is experiencing it's unwanted outage, bypass the battery cables completely with jumper cables and see what happens. Or just replace them with new out of spite.
As was written above, make darn sure your battery has a good ground to the frame. Unfortunately, 40s are cursed with a battery frame ground point just inside the passenger side fender well, where it can be exposed to everything from mag chloride to mud and all kinds of stuff. In my experience, once a good ground is established there they are usually good for a decade or two, but if that connection has been disturbed and not reconnected with proper metal surface prep it may only last a few years.