It's not "Webmin" the app, but a generic webmin. Not sure about the terminal, I have not enabled remote management and it's refusing an ssh connection attempt. Maybe not possible? Logs are filled up with "Cant find NTP time" every 6 seconds (even though it has the correct time), and only go back a day or so.

Is this an ISP provided router, and is the NTP thing a problem/the problem or just a nuisance because it's filling the log? The log on my router doesn't record wifi start time or anything like that. It records that it's doing a check on 5Ghz channels for any interference with radar, but that's it. It appears to truncate/delete the log on shutdown, so log start (on my router) is uptime start.  My router also refuses SSH.

There's no such term as "a generic webmin" - nobody on the searchable web has used that term in the context of web hosting control panel, nevermind referring to a router management interface - only for referring to the product Webmin.

Anyway, is there any name or logo that identifies what software it does use? (Might only be on login page, or on an about/credits page, or in a footer, or maybe only in HTML source).

If so, maybe there's documentation for it that can point towards an answer. Otherwise, if you can't find/enable a way to type commands, and all the logs are fully clogged, I can't think how to obtain the current uptime. Obviously, fixing the time servers and/or firewall to stop the NTP log entries (or even updating config to check less often) might allow that method to work going forward.

It's a belkin router with belkin's firmware and web-browser-admin app. I dunno what the deal is with the logs. It's not falling over but I wanted to check when we had an anticipated power out.

Sounds like either the NTP server setting in the web admin thing is wrong or missing or something, or the server it points at is borked. Doesn't matter that it has the right time, it will always check the NTP connection. You could point it at time.google.com just to check. It's tucked away in the Network Settings on my box. You say the log only goes back a short way, my guess is that the start of the log is the start of uptime. My router (a Fritz! Box) displays internet connection time on the first page you get to, but start of uptime, ie the start of logging is (not surprisingly) in the log. It's 6 February at 15:03:29 thanks for asking.

Make and model?

Belkin N300