1965 Dart Charging System Question

Am I right in thinking that the ignition wire between the ignition switch and the bulkhead connector is 16 gauge?
Probably. Certainly not smaller. 14 ga would be OK too.
I made that circuit diagram based on the '67 Barracuda and Valiant wiring diagrams.
1965 has some differences at the bulkhead connector and there are probably other differences as well, but probably not the ignition feed.

There's a scanned '65 Plymouth service manual here.
MyMopar - Mopar Forums & Information - Service Manuals
If you have bandwidth, download that and check the Valiant diagram in the back of the electrical section.

Both ends of that wire are probably Chrysler or Packard 58 type female terminals.
It's not too difficult. Make it up on the bench and then install it.
Unwrapping the harness tape may not be any fun. I've cheated a few times by leaving the orignal wires in the harness and runing the new wire next to it. Tape or gently zip tie to keep it neat.

You'll have to remove the bulkhead connector on the engine side.
Then with a hair pin or release tool, depress the retaining tab on the terminal. Give it a little push and then go under the dash and it should be free.