The new switch came in, I gave it an appropriate DeOxit bath, did the "flick-the-switch-100 times" cleaning, and followed up with DeOxit Gold and more switch-flicking. Installed the new switch, checked my work with the dim bulb (checked good) and then fired it up.
The relay clicked within a couple of seconds. Awesome. (There was no relay clicking when the switch was missing.)
Took readings off L1 and R1. They are:
L1: +5.2 mVDC (took a while to settle there)
R1: -1.3 mVDC
I tried to read the schematic, but ended up scratching my head. Where do those readings point towards? Hey, at least they aren't both reading +41vDC anymore!
Oh, I haven't installed the new resistors yet, I thought I would tackle one change at a time first.