Turn Signal Relay Issue

I think I'd start by diagnosing the brake lights. In most early Mopars, the brake light filament in the bulb (1034's or 1157's) is the same one as the turn signal uses. The turn signal switch just cancels out one of the stop lights depending on which way you move the lever. The turn signal circuit depends on load for the flasher to work. Either use all incandescent and the stock flasher, or, the LED version with the LED bulbs. I wouldn't try to mix and match.

Thank you for the insight.
I will test the Socket in the trunk tomorrow. I looked today in the trunk floor and the wall along the bumper. I could not find any ground wire bolted to the trunk pan. The wire diagram shows a Ground Wire ring terminal on the read defroster motor, but I could not find that.
I only see the bundle of the Violet, Dark Green and Black. The Black seems to be the series carrier wire.
I am not sure what the upside-down Xmas Tree symbols are that are under each rear bulb, in the diagram.

I was going to take a short pig tail wire and attach one to the silver metal light housing and the other to the trunk pan, to make an extra ground connection.

I still cannot figure out how to remove the stop Light Switch, to replace that part. I have turned the cylinder of the switch, but it does not pull out.

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