I have used several Painless kits but on Custom builds and they were more universal and all of them used a GM steering column plug.

All of the early Mustangs I have done we used the Mustang reproduction harness that matches.

In the big scheme of things there aren’t that many wires that go into the column and if you know what each is on the harness side you have it wooped.

Just take your time and solder some good connections that are removable. Wiring can be overwhelming as a complete task but rather easy one wire at a time and very satisfying once completed

I don't have experience with the issue you're having but can send you the OEM wiring diagram for the steering column plug.  PM me your email address if interested. 

The plug with the color stripe next to it is just like mine. The other is painless.

wsinsle wrote:

Looking at the color code on your plug coming from the steering wheel (not the painless) it matches my 66-wiring diagram. Looks like its original as you said. What I'm going to post is from my 1966 wiring diagram not 65.I think the 65 had only 1 dash turn signal light, not 2 but I may be wrong. The painless may use different color wires but the plug could still be right.

Your White/blue should go to painless Front Right Turn Signal and dash turn signal light.
Your Green/white should go to painless Front Left Turn Signal and dash turn signal light.
Your Blue/yellow should go to painless; this goes to the head light switch. The head light Sw. has a circuit breaker and supplies + for the horn.
Your Yellow goes to painless Horn wire.
Your Green goes to painless Brake Switch to supply + for the brake lights.
Your Blue goes to painless Flasher to supply + for the turn signals.

Hopefully painless supplied a good wiring diagram and you can see if the plugs match up. There is another 2 wire plug that goes to rear turn/brake lights.
 

The 65 did come with one lamp for both left & right turn signal.  This is a dual filament bulb and the wiring is the same for the 66 turn signals. 
So, it is correct that the White/Blue wire is for the right turn signal and the Green/White wire is for the left turn signal for both the 65 & 66 Mustangs.