1964 Valiant No Brake or Parking Lights

i am in a similar position with my 1968 Valiant. Working turn signals, but no tail lights or brake lights. I have no idea how long it's been off the road, I suspect 5-10 years.
It could be that both the headlight switch and brake light switch are bad. I've had both those fail separately on other cars. Oddly the headlight switch fails and only the marker lights were affected. Another thing to consider is that the brake lights go through the turn signal switch and a failure there can take out a brake light though the turn signal still works. I've had that happen but only to one side on other old Chrysler products.
The other possibility is the bulkhead connector. I had lighting issues there on the 1967 Valiant I used to own. While the wiring was nice, once I opened it up there was lots of corrosion. It was so bad I had to get connectors from another harness to replace the severely corroded ends on my wiring (back before new harnesses were available and much cheaper any way).
I haven't dug into my 68's problems yet. Good luck!