Basically what it says in the subject. I'm using a Red Hat 8 machine without any kind of power saving business enabled to intercept the power button; when I press the power button the machine turns off instantly. Since there's no chance for the system to record when the power was shut down, is there some way to infer it? The closest I've come has been using /usr/bin/last to figure out when I last pulled up an xterm, since I do this often when using the machine. However, inactivity would have the same effect as a switching off for the wtmp/utmp logs. Is there a better way?

I really wouldn't reccomend shutting your system down like that with your filesystems in rw mode.

Try shutting down with:
shutdown -h now

Yeah, most of the time I use halt -p. It's just that there's the occasional instance where a program like firefox runs away and makes the machine unresponsive.

If that was happening I think I would try and find out why.

Another simple solution would be to write a log file every 5 minutes with a cron entry like:
*/5 * * * * date > /var/log/up.log

Then you can just take a look at the log to see when the system was up.

Thanks for the advice!