The panel lights work off the S-1 connector on the light switch, not the S-2 connector. The S-2 connector is for the headlights only. Randall's wiring diagram clearly shows that. The switch is designed so when you pull it out to the first "stop", side lights come on and and panel lights come on, if you have the push-pull panel switch "pulled". When you twist the "side head" switch 20Âş clockwise and pull again the headlights come on and the side lights stay on.
Arrow, I give you credit for doing your own wiring harness ! When I did my TR3A restoration, if there was an aftermarket wiring harness available, I sure couldn't afford it. My budget was aimed at more important things (drive train!) Fortunately, there had never been a major "melt down" in my wiring harness. I removed it from the car, stripped the vinyl wrapping (post 70.000) back far enough to see brightly colored (color coded) wires, cut and moved them out of the harness so they were visible at the external connector(s), spliced in generic red or black 14, or 16 ga. inside the harness, and then re-wrapped it in vinyl. All connections soldered and shrink-wrapped. It looks great but if you were to open up my harness, there would be nothing but red & black wires!
I think Lucas made the harnesses back then, so there were lots of "short cuts", especially with grounds that are frustrating to the restorer.