'67 Dart - No stop lights, turn signals on but don't flash

Hey thank you for the links, that's a great read, a lot of very relevant info, much appreciated.

Today's update:
The new turn signal flasher unit arrived in the post so just been out to try it. I tested this new flasher with 2x21W bulbs in parallel across the battery and it flashes ok as expected.
I fitted the flasher into the turn signal circuit and ....... no flashing, just constant LH or RH turn lights.
I got the multi-meter out with the intention of ensuring that the polarity of the flasher is correct for the circuit (should be standard pins but checking) but found unexpected voltages.
The battery is showing 12.14V. Probing the turn flasher harness socket with ignition on and left or right turn signal on: from ground to the black wire shows 11.93V, from ground to the red wire shows 0.01V. Pressing the brake pedal made no difference to these voltages.
Mike69cuda you suggested that the flasher switch is likely to be faulty, and yes, I've fiddled with the switch and if I flick it up for on and then nudge it down slightly the front RH bulb will come on making all 4 working. Thank you for the hint there, new switch in next parts order.
I have tried many combinations including turns, 4-way, stops, ignition and discovered that with ignition off and 4-way flashers working nicely, if I press the brake pedal then the flashing stops, the 4 corners stay on.
I'm thinking that there must be a a short somewhere (or ground fault?, don't understand those, strange things happen).
* Could the turn circuit be picking up power from a short so that the flasher is bypassed?
* Does the stop lights making the 4-ways go constant support this?
The most accessible place where the stop and turn circuits meet is in the tail light sockets? I'm not too happy with the tail sockets so I'll try remove one bulb at a time.
RedFish thank you for the Summit link; if I need anything else from Summit I would buy those but I have stuff that I'm getting from Rockauto so I have done some searching there for tail light sockets. Nothing is listed for the Dart tails there so I looked for models with the 1-1/8" reflector hole. It looked as if there were some Ford (& Chev) tails of that era that may suit and this lead to this article:
Microsoft Word - Silly Sockets.doc (corvair.org)
This lists the Chrysler part number 2926370 and this leads to STANDARD MOTOR PRODUCTS S75 and DORMAN 85860 on Rockauto. Both quote 'Alternate/OEM Part Number(s): 2926370' and have the ground tab. I'm going to order both of these, hoping that they fit ok and see which look best quality, bayonet, springs, contacts etc..