Tail light gremlin
This will help with diagnoses
https://www.web.imperialclub.info/Repair/Lit/Master/index.htm1967 Accessories Circuits (#236)
On your model the parking lights and and tail lights share the tail light terminal on the headlights switch.
In other words, with one click out and two clicks out (headlights on) position all of the marker lights should be on.
The only relation between the turn/stop circuits and the park/tail light circuit is the bulbs share a ground.
Always worth checking the bulbs are correct type and positioned properly in their sockets.
If a ground is not available for any bulb, the electricity will find another route to complete the circuit even if it has some resistance (like the other filiment and another bulb)
If you want to check the turn signal switch itself, disconnect at the connector, then check for continuity and write down what you find. Using the '67 turn signal switch diagram as an example:
With the switch in the left turn position:
Position 2, Power from flasher, to
1 continuity
3 no
5 no
6 continuity
7 no
8 continuity
Position 7, Power from Brake switch to:
1 no, 2 no, 3 no, 4 no, 5 no, 6 no,
8 continuity