It sounds to me like you have a break in continuity in the wires that carry the brake light and turn signal voltage pulse from the turn signal switch to the left tailights. Let's concentrate on the turn signals.
There is probably a bad connection in the wire(s) as it passes through one of the two main wiring harness connectors (junction blocks, or harness plugs). One, I think, is inside the car near the fuse box under the dash, probably to it's left; the second is on the rear bulkhead just forward of the antenna. I am frankly not sure how accessible the rear junction block is with the exhaust system and spare tire tub, etc in place.
You're going to have to trace the wires back to the turn signal switch.
Here's what I think can be done to narrow the possibilities (I used a 63 shop manual to check the routing, so it's possible the 67 may not match my description):
Use a multimeter on the 12V DC scale, attach the minus lead of the mutimeter to a clean frame ground, and use the positive lead to check the wires that activate the turn signal light blinking. I think they are violet-colored wires attached one to each right tailight. With the right turn signal activated, you should be able to tell if you are getting the voltage pulse at the ends of those violet tailight leads.
If no voltage there, then check the turn signal switch near the base of the steering column... turn the ignition switch off, remove the harness connector and clean the contacts on the harness connector and switch, and replug and check. If that doesn't help I think the wires for the turn signals (probably purple for the left tailights and violet for the right) plug into the "middle row", or pair, of connectors on that switch. With the harness disconnected from the turn signal switch, you will have to provide a 12V lead to the center connector of the row that has 3 connectors; alternately you might be able to use a sharp probe on the multimeter to pierce the wires you need to check while leaving the harness connected.
Use your multimeter (with the negative lead connected to a clean frame ground) to check the purple-wire's connector (on the switch) for voltage pulses when the left turn signal is activated (since the left works, you should see voltage pulses); then do the same for the vilolet-wires's connector while the right turn signal is activated... if no voltage pulses, then perhaps you have a problem in the steering column. But if you do have voltage pulses, then as I suspect, there is a break in the continuity of the violet wire somewhere, probably in one of the two body harness connectors I mentioned above... one will need to be opened and it's contacts cleaned (you can check/eliminate the one under the dash with the multimeter to see if violet-wire voltage is getting to and through it).