The firewall side (not being replaced) side has the female terminals.

The terminals, if needing replacement, are closest to Packard 58 not 56, in most of the cars I've looked at (late 60s). Some call these Ford/Chrsyler terminals.

https://www.repairconnector.com/products/Universal-GM-Chrysler-Ford-Female-Terminal-Connector-20%252d18-AWG.html
https://www.repairconnector.com/uni...ale-terminal-connector-14-12-awg-5-pack/
http://www.texasindustrialelectric.com/_packard_terminals.asp
https://www.mouser.com/Aptiv/Automotive-Connectors/Series-58/_/N-1z0zlezZ1ehb5Z1y9jlfy
https://picocanada.com/en/products/181 (canada)
Get a proper crimper for "open barrel" terminals. Astro-pneumatics is cheap and has interchangable jaws. However the jaws are too wide to fit on OEM and some aftermarket male terminals. The packard crimpers and copies are good but often expensive. American Wire sells and rents these crimpers.

Save the original harness. Its useful for reference and parts.
When the replacement harness on my 67 started to show some issues, I had to replace a few terminals. Some were packard 56. The original harness was 58. So I used the 58, but then the 56 connector was loose. Fortunately I could take the original connector from the original harness and all was good. Small differences, but sometimes important.

Mattax good info

I don't know if anyone answered, the circuit breaker is in the driver side kick panel.

while wiring might be causing some issues, you could probably wait for them to shut off and then try tracing back the wiring till you find voltage again.
that might help you narrow down the "bad" part to start with.
Do the high beams work when this happens?

No, high beams were on when I witnessed it.

Makes it sound even more like a breaker problem, whether in headlight switch or elsewhere located.

An overload can not be traced by looking for voltage after a fuse has blown or a breaker opened.
Fuses open when there is too much current running through them.
This only happens when there is something drawing too much current, or a shorter path to ground downstream of the fuse.

And lets see this headlight breaker somewhere other than in the headlight switch for 69 Dodge Plymouth or Chrysler.

that is true, but you can tell where to start looking by tracing voltage.
if it stops at the switch, or if it stops at the breaker, you know it has to be down stream.
and can eliminate something from your search.