After a ton of help from Dan here, and the support at GarW, here's what I can say:
I have confirmed A3 and the illumination line on the start button have continuity. They are on the same line, which would explain this whole mess. Of course, that does not explain where the break in the line is occurring.
I remembered that as I was working on this car originally, one of the fuses was melted, under the dash (you'd think I'd remember that, but I've been messing with all this for months, on and off [mostly off]). As far as I remember, it was the interior fan. I can't know for sure, but based on this KFC wire, in the picture below (first wire on the left), I'd say it's a safe bet:
I checked the interior fans, and they're all good. Could this be the wire that leads to A3 and the ignition illumination? Who knows? Probably? But if the fans are capable of coming on, and they were still connected to this, you'd still have voltage on those lines, but of course, there's not.
So, what to do at this point... well... I have a few options:
1. Try to splice into the interior fans line, somewhere (assuming I can find it, close to the instrument cluster), or just run a new wire, directly from that fuse panel to A3 and the starter illumination (who cares, really - if you bridge the starter, it stays on all the time anyways).
2. Splice into the radio ignition line, and run a short line to A3/starter illumination.
The difference is going to be the size of the fuse, obviously. For the interior fan line, it's a 20A fuse. For the radio, it's 7.5A.
I can't imagine the instrument cluster needing more than 7.5A, combined with the stereo.
As I discussed with Dan, I should probably chop the line at the instrument cluster, and tap in there. This way, if the wire melted somewhere, it won't short to other lines, or ground (whatever the case may be).
I'm dying to find out, but this may have to wait until I get back from a ski trip this weekend...
And not that this matters, but it appears to be line 19 O in the diagram below:
This means it's Fused Ignition, Splice B - for whatever that's worth.