Mystery wire in headlight harness

Well that diagram is OK, sometimes, but not to be relied upon.
When you get to one of these head scratchers, factory service manual is the best source to begin with.
Then, although harder to read, the assembly drawings (published by Faxon) have many of the harness details.

I assume from your photo this is '69 Dart???
Yes it matters. Dart, Valiant, Barrcuda all had different wiring details those years.
'72 Harness is unlikely. Obvious differences ito look for will be the triangular plug for the ground controlling voltage regulator (starting 1970), and the 5 wire pentagon shaped plug for an ignition ECU (phased in '72 Model year IIRC).

Let me get you a link to a good version of the factory '69 diagrams.
There may be more info in the paper copy but IIRC this covers the wires and most of the identification codes.