You can always upload your photos on imgur or another hosting website and link your images here.

No idea on the connectors though.

Haven't had a chance to *take* em 😉

I live in an apartment with subsidized rent and I have an inspection tomorrow. It's gonna be a couple days, I need to clean and then I need to sleep...

From looking at the service manual and oldcrap website, I'd say you're right.
Probably a 16bit ISA slot on a 50pin IDC connector.

Gotta be ISA-8. Look at the number of pins.

ISA-8 = 62 pins
ISA-16 = 62 pins + 36 pins = 98 pins

50 pin IDC + 10 pin IDC = 60 pins

So either it's ISA-8 minus its two front teeth (LOL) -- I'm not sure specifically which, but T/C [Terminal Count], CLOCK [System Clock; see below], /REFRESH [DRAM Refresh Signal - Active Low; see below] /NOWS [No Wait-State - Active Low], and RESET [Duh!] seem prime candidates for sheering off here. Why "System Clock"? Because you can compensate for that with careful VRAM access timing and a couple 74xx244 or 74xx245 latches real easy like... or expensive double-port memory if that's your thing 😉 Why /REFRESH? Because VRAM, in my experience, is almost always if not always Static RAM... TBH I've never seen DRAM used in the wild, but I'm not well-traveled enough to be an authority there and I want to be clear about that. Also worth mentioning, there's a single pin each for -5vDC, +12vDC, and -12vDC -- if any two of those were deemed spurious and eliminated, that would do it quite nicely, and leave *all* the signal pins.

That said, I've not got a magic bus identifier here in my back pocket -- so I'd have a hard time working this one out on my own. Any suggestions for an easy way to tell?

The other 10 pin IDC looks like it is more for an external display connector, so the bus should only be on the 50 pin and considering it's specific to this machine and only for display, it won't have all of the isa signals, so you can remove all the dma lines, all but one irq line, etc...
so yeah ISA8 wil probably suit it best.

OK, I have an auditory logic probe, a dedicated continuity tester, and a number of multimeters. For right now I'd strongly prefer to keep this out of an actual Compaq Portable III, although I do have one such machine -- it is not operational right now, however, and it has display issues as part of that at the moment. While going into any further detail will inevitably result in a rant long enough to *gratuitously* exceed the per-post character limit, simply due to the sheer quantity of aggravation I've had off that one system, suffice to say that at this time, that's not an option I'd relish. I *do* however have a spare motherboard as well...

So... given that equipment and nothing more, what's the easiest way to work out what signals are present and what the pinout is?

no idea. just guessing.

easiest to test continuity on would be the ground and power lines... if you know which are which, though 5v and ground should be simple enough.
also reading the comments on the oldcrap website shows the display needing 200v, unsurprising since it's gas plasma display.

HV is on a separate connector 😉