This car also has the front side marker lights options so that means an additional wire to the turn signal switch
Assuming you mean "cornering lights", the light on the side of the fender that comes on with the turn signal...
So, I looked at the Shee-Mar catalog and the parts book again and noticed that SM107 also fits the Imperial. The Imperial has cornering lights as standard equipment, so it would seem that the SM107 might have that wiring.
I googled SM107 and Shee-Mar has a picture of the switch.
SM107 – www.Shee-Mar.com
I count 10 wires coming from that switch. Looking at the wiring diagram in the service manual, I see that the turn signal switch has 7 wires, 1 of which will be the horn.
Tracing the wiring from the cornering lights, I see 2 empty sockets on the connector to the TS switch. Lt green w/tracer and tan w/tracer (stripe) are the wires from the cornering lights.
Front end wiring diagram showing cornering lights. This shows that the wiring goes to cavities 17 and 21
So now we look at the switch right from the Shee-Mar website.
Again, I count 10 wires coming from it. The switch in the Chrysler wiring diagram has only 7. This makes me think that the Shee-Mar switch is already wired for the cornering lights.
It would make some sense to look at the existing switch and count and compare the wires.
If this was a $20 switch, I'd say just gamble the 20 bucks.... It's a $100+ switch, so if it were me, I'd want to verify. Maybe a call to Shee-Mar might help, but it also might depend on who answers the phone if you get a correct answer.
All this said... Are you sure the switch is bad???