Did the day shifts not have a standard start time, or were all the hours completely chaotic from week to week?
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There's also the bonus of two synonyms for 12 which are especially dispositive; "I start at noon on Wednesday."
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I asked above if you had regular daily shift hours because that's the type of thing your S/O would have known. If 12-8 was your regular shift, it would be implied (you might even skip the times and just say, "the usual shift" or something to that effect). ....
Let me take it from the hypothetical and put it into the real...
I worked in a resort town, where everyone's shifts were chaotic. I actually had fairly regular hours.... 3 days a week I worked 8am to 4pm, and then on the 3rd day - the day I worked until 4pm - I came back later that day and started 2 evening shifts - midnight 'til 8am. I
could have chosen to work the noon 'til 8pm shift - but then I wouldn't have had the ~2.5 day weekend. This is not a hypothetical - it's what I worked... and I gotta tell you it was murder on the system switching from the night to the afternoon shift each week. On those shifts when I was filling for someone else, there was no context to get the time right... I would nail down explicitly - and repeat back to the front-desk manager in a different way - whether we were talking AM or PM.
I was not alone in this issue. It was a resort town, and people worked all sorts of hours, split shifts, and double shifts. One time when flu hit our hotel two of us were left standing, and we basically swapped 8 hour shifts. So, 8am 'til 4pm - back at midnight 'til 8am - back at 4pm 'til midnight - back at 8am 'til 4pm.... for 3 days.... thank God it was a 3 day flu and not the 7 day variety. AM and PM became - well actually, it didn't matter. By the 3rd day we had no idea if we needed to greet a guest with "Good Morning, checking out?" or "Good Afternoon, checking in?"
You are perfectly correct, I would have used noon and midnight - not 12 and 12. However.... if the hotel had used shifts starting using an 11-7, 7-3, and 3-11 then noon and midnight wouldn't have been relevant.
My "wife" in my example came a few years, later - so for my earlier example she was a "hypothetical"..... since it was a hard partying ski resort town - tone of voice would have been meaningless ... was I unhappy that I wasn't skiing, or heading out to a party..... who knew? And when I say "hard partying" I mean I bumped into friend of mine at a house party and asked him how long he had been there. He thought for a moment, and then asked what day (of the week) it was. No kidding.
Or.... then there was the day I popped into town at 10:00, met some friends at the King Eddy and had a couple of beers.... before finally ending up at work a couple of hours late (it was OK, it was the last day of training for a new hire, and I called her to tell her I'd be late.) At 3:00 I finally got to work. Go ahead, parse that without the AM & PM 'cause you'd be wrong, likely. Met the friends at 10AM, and finally ended up at work at 3AM (Like I said - it was a hard partying town).... luckily she was fine, and since it was the night audit shift and I could just sleep it off in the staff room. She woke me just before management arrived and I scooted out (being careful to be seen
from a distance) as management arrived. As I recall, that was not one of my better skiing days....
Would you believe that I was actually one of the more responsible employees? Sad but true.... but that was the only time I showed up to work even a little bit, um, 'happy'.
Update
CalBoy .... I actually mostly agree with your point that people seem to do just fine with the 12 hour clock, vs the 24 hour clock.... but you did issue a challenge

..... Really, the only time - imho - that the 24 hour clock as an advantage is calculating durations in your head. For 8 hour shifts that span noon, it requires a bit more mental arithmetic to get the times right. Doable, just a bit more work. I had to check and double-check my 7-3 shift example above to make sure I added the extra 2 hours to take it out of the normal base-10 arithmetic. Minor, sure.... but the 24 hour clock is bit easier there.