I don't think 53 Chevy trucks came from the factory with turn signals and maybe not even a right rear running and brake light. Usually, aftermarket taillights combine the rear brake light and turn signal functions to a single filament on each side. If so, your turn signals working eliminates any problem with the brake lights being any further towards the rear of the truck that the turn signal switch.
Do you have a voltmeter or a test light? Except for inside the turn signal switch, this is easy to test using either.
Yes, they are add on’s with the turn signal. They were working this week except the parking lights. I know because the right rear had 2 broken bulbs that I replaced.
The blinkers work front & rear.
Odd thing is (this is an old thing). The R front blinker blinks if the head lights are off, head lights on, it stays on & don’t blink.
I’ll crawl under the truck when I get going today and follow the tail light wire.
Thanks for advising!