So no visible clock... But also no visible indicator of how long it will go on... I might prefer the incorrect time to that...
Most of those are synchronized to the grid, and the grid keeps time really, really well. They actually synchronize the grid to atomic clocks etc for that purpose.
I'd wager all of them get timing from an internal oscilator driven by a low-voltage DC supply and have no mains frequency or voltage anywhere near them.
Where do you live that you have frequent enough brown outs to notice these things?
I have a time switch. It looks entirely mechanical, but I suspect it gets its time signal from the mains: it doesn't seem to drift at all. If there's ever a power outage (which happens from time to time when our breaker trips, not because the real mains is down) it just stops advancing the time, but doesn't reset, because it's all mechanical.
Where do you live, and how old are your oldest electronics?
Anything that uses DC would likely have at least some capacitors in them.
https://hackaday.com/2018/03/29/ask-hackaday-is-your-clock-t...
The US doesn’t mess with time in some states, including where we live (Arizona).