So, anyhow, I set the SGI to autoreboot at 7:30pm, given that it has a command to do so (although the man page didn't seem very confident about whether it would work on an O2). And, later yesterday evening, I tried pinging it, but it wasn't pingable. The Linux box, on the other hand, didn't have such, so I didn't even bother trying it.
Thus, I was a bit surprised to find that the Linux box was happily up and running when I got here. It didn't need any poking at all, really; everything runs fine.
And the SGI? Well, I remembered when I got here and saw that it was powered up (but still not accepting pings) that it doesn't like to boot if it doesn't have a keyboard attached. So, I powered it off (soft power switches, when done well, are quite useful), attached a keyboard, and powered it back on. Shortly thereafter it made a happy SGI chime, and then a minute or so later it was accepting ssh connections and incoming mail. I have the maillog on a tail -f in a console window; wow that's a pile of mail!
Sigh. For lack of plugging in a keyboard, and a little bit of knowledge of how these machines react to power outages, I could have saved myself a trip. Ah, well....