Here goes
My rear blinkers, running lights and brake lights all work, sometimes.
If I last made a left turn and used the turn signal and even if the turn signal has canceled the RIGHT rear brake light will not work.

If I last made a right turn and the dash turn indictor has canceled both brake lights work fine.

Years ago when I took an old turn signal switch apart I found that the connections are made by slides moving in plastic tracks the slides and each end of the track have a brass foil which connect with the different circuits.

The switch uses the same filament for both brake and turn. That means that if the turn signal is canceled there should be contacts to provide power to both tail lights when power comes through the brake light switch.

I saw something like this on a German car when the steering column bearings went out and there was play in the steering column. While it sounds like the switch the one I have in has less than 10,000 miles. I can get a switch at OCPNW (thanks Ray) but they are spendy. I don't see this exact problem in any of the blogs.

One other electrical question: On the FSM wiring diagram they show a trunk light. On my 64 convert I do not see evidence of a trunk light or switch any where in the rear harness. Usually the FSM notes if it applies only to a certain model. I don't want a bare wire somewhere. But I can't fine one.

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64 Dart GT Convertible, 225 Super 6, Carter BBD, 14x7 SBP Rally Wheels, HEI, Fuel mod, wiring upgrade, Alt upgrade, 2BBL, headlight upgrade, front disc brake conversion

Trunk lights were always optional on a-bodies.

I also suspect your turn signal switch, and I highly recommend spending the money on an NOS one, or buying one of SlantSixDan's reproductions.

Link to Dan's for sale page:
http://www.slantsix.org/forum/viewtopic.php?t=53183

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Casually looking for a Clifford hyperpak intake for cheap.

Yup, Reed is right, you need a high quality new directional light switch.

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67' Dart GT Convertible; the old Chrysler Corp.
82' LeBaron Convertible; the new Chrysler Corp
07' 300 C AWD; Now by Fiat, the old new Chrysler LLC