Yes, I agree with your plan. The "low side" connection of the socket is through a fixed resistor when nav lights are ON or direct to ground via the nav light switch if nav lights are off thus making the lights dim when nav lights are on.
So, I had it backwards and the switches connect to positive voltage on their common terminals, which complicates things slightly. But it's still a workable plan. And I am thinking about changing out or short-circuiting that stupid resistor while I'm at it...I wonder if I can find an IA to sign off on that. I've never been landing at night and thought to myself "I am sure glad those gear indicator lights are extremely dim, that really inspires confidence!"
But basically I can leave the panel light switch off and test the following resistances:
A - Left neg to ground: should be close to 0
B - Right neg to ground: should be close to 0
C - Nose neg to ground: should be close to 0
D - Left to nose: should be close to 0
E - Left to right: should be close to 0
F - Nose to right: should be close to 0
If A, B, C, and F are all 0 and both D and E are significantly above 0 and similar to each other, then I will have isolated the problem to the left main switch and its wiring. If all of these are indeed close to 0, then the bulb socket is the most likely culprit. (Although I really do suspect the switch since it lives out in the elements, gets an oily bath if the strut leaks fluid, and otherwise has probably had a much rougher life than the bulb socket over the past 50 years.)
It looks like switches are reasonably priced in airplane terms:
https://www.knots2u.net/switch-down-limit-main-gear-piper-67411-04-67411-004/