Electrical points burn with use. In these early cars they didn't use relays to handle the heavy electrical loads at the switch so they generally burned up after a few years of constant use (if you never drove at night or in fog or rain they lasted longer). The factory coated their points with tungsten to allow them to last longer. The Chinese importers don't do that as it adds cost that they would rather keep as profit. In this regard an AC-Delco branded light switch (assuming it isn't counterfeited) would get you a better quality part.
The other switch in the circuit is on the floor where it is exposed to not only high amperage switching, but dirt, grime and water. It isn't used as much (some like my wife, never use high beams) so it may have died years ago, and you wouldn't know it until you used it for the first time. Then it fails miserably, because the springs that maintain contact between the points have rusted away.
There is a chance that if only one bulb is flickering it could be a broken filament that touches intermittently to burn when in contact and flash out when not touching. Chances of both doing that simultaneously are slim.
Finally your wiring was suspect the day they built the car. The days of finding copper ore lying on top of the ground are long gone. Deep hard rock mining, or huge open pits that are up to a mile and half deep are used to expose copper ore which makes copper a very expensive metal after WWII (the reason the factory uses aluminum in their radiators today). The factory used the bare minimum length to reach, and then undersized the wire for the load when they built your car new. Add a half century to stiffen the experimental PCV insulation used on the wires, and oxidize the copper strands and you can see why it is suspect. Vibration and movement due to rotted rubber insulators and you get broken wires and wires pulled out of terminators.
Most mechanics will not touch electrical problems because they are so time consuming: it isn't worth their while. There are specialty shops that work only on automotive and marine electrical problems, but they generally spend their time, and your money, by replacing all of the wiring with a new wiring harness and replacing all of the switches.
Here is a hobbiest version of a professional probe that I use in conjunction with a twenty five foot ground wire to find automotive electrical faults: