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I have never seem a 24h wrist watch (I know they exist) aside from extremely seldom as wall clocks
I've looked for them, but they're very hard to find and expensive too. You can't just slap a 24h face on a 12h mechanism, so it's all custom and produced in low volumes. (I think it's technically possible to convert a 12h period into 24h by switching out a single gear, but that might ruin your minute hand too? I'm no clock maker.)
They don't have to be expensive, though such watches are less popular for everyday use. In fact I'm wearing a Vostok Kommendurski with a 12/24 hour dial. When I was a medic, I needed to record all my times in 24hr format on my run reports. I think I paid $35US delivered from Russia 15 or so years ago.
And no extra gear is needed to make an analog watch/clock indicate 24 hour time. Time doesn't change. You simple have one scale that reads from 12AM through 12PM and then at the next hour, (1PM) it simply gets renumbered to 13, 14, 15, 16 and so on until you reach 24 on the inside scale. Easy peasey.
But it is possible to build a watch/clock that the movement does move in 24 hour time and you would be correct it would a couple of extra gears to accomplish. But, it would also be a real pain to create a legible watch face with all those numbers on a reasonable sized watch. Far simpler and easier to print the two scales on the face and call it good.
You paid $35 for the watch, the delivery or both? Because I saw those Vostok watches with proper 24h faces, which is exactly what I'm looking for, but they're $140. I guess that's not super expensive for a watch, but I can get a much nicer 12h watch for that money.
And a double numbered clock face is the simple solution, probably more convenient to read, but also not really a conversation starter :)
Vostok Komandirskie
I paid $35 delivered from Russia. And honestly, I do not remember if that was a sale price or not because it's been enough years ago now.Despite all the cheap quartz watches found in Walmart, $140 really isn't all that much for a properly made manual wind watch these days. Even a plastic Timex will set you back nearly $120 for a quartz LCD with 24 hour display and only one choice of looks. So I probably wouldn't consider the price out of line for the Komandirski with multiple choices available.
A Bespoke 24 hour mechanical movement would be quite the piece of horology art. A conversation started indeed.