The rear tail lights and the front parking lights wiring, are separate from the turn signal switch.
They both are fed from the headlight switch.
On the headlight switch there is a terminal for the rear tail lights and a terminal for the front parking lights.

The brake light switch is fed voltage from a terminal on the headlight switch.
The brake light switch is connected to the turn signal switch.

The turn signal switch, switches between two sources:
1. The flasher module
2. The Brake light switch

What is the model of your signal stat add on directional set up?
Do you want to make your signal stat add on directional set up function?
Are your rear tail lights and the front parking lights working?

Note: Attached photo wire colors apply to 1954-55 1st signal switch color scheme.

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Attachments
turn siginal switch schematic.jpg (97.22 KB, 206 downloads)
headlight switch.jpg (47.45 KB, 206 downloads)