Unfortunately, I've experienced some similar things with my '67 Chrysler. First time it happened, it turned out to be some splices that a previous owner put into the red wire going to the ignition switch. Even covered the bare wire with the "famous" chewing gum paper! When that joint of bare, twisted and somewhat tarnished copper wires would get hot, too much resistance and the circuit was interrupted. When it would cool off, it'd work again. I fixed that situation and things were fine for a time longer.
Also check where the red wire plugs into the bulkhead connector on the inside. It might be a little loose down there. Some cleaning and tweaking of the female terminal might be necessary.
The other thing is to fully take the cables off the battery terminals and clean them with a wire brush cleaner and then reassemble. I discovered a really thin coating of gunk that had accumulated between the post and the cable end to be causing a sudden no-start problem there too. After I put the Chrysler electronic ignition kit on it, it started for 5 times with no problem, but the 6th time it did nothing. It was in that diagnosis that I also found some other splices in the red wire that I hadn't previously found too.
For the ignition switch to work fine, it has to have a good voltage and amp supply via the red wire to the switch.
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