According to reports of the time;
When the children arrived, a priest looked at his timepiece and complained it was already after 12 noon and that
Our Lady wasn't coming, everything being just a hoax and everyone should go home.
According to O Dia newspaper, "At one o'clock, the hour of the sun, the rain stopped."
Another witness, Dr. Almeida Garret, professor at the University of Colmbra in his testimony stated the people looked up and it was "almost two o'clock wartime or about noon, sun time".
To estimate the exact time of the sun you would have to know what war time was. Maybe it was something like daylight saving time.
Anyway, Our Lady wouldn't have used a timepiece, she would have used the sun.
In those days poor people didn't have watches because they were too expensive. So most of the people in the crowd would not have had access to the time by mechanical means, nor would they have been accustomed to thinking about what time it is out of daily habit. They were used to gauging day time by the position of the sun in the sky.
But from the accounts I have read, the expected time of the last apparition had passed without the apparition having happened, for whatever reason. Perhaps Our Lady was answering prayers of latecomers who didn't want to miss out and were hurrying through the muddy paths, in the rain. Perhaps she was sympathetic to the cripples whose mobility was greatly diminished in the rain, at least some of whom Our Lady had planned to heal that day. And perhaps she was giving that one mysterious priest one last chance to accept the grace of conversion, even though he turned out to reject it in the end.
The unidentified priest who attempted to make everyone go home when Our Lady's arrival was delayed was probably not the parish priest who had been giving the 3 children such a hard time. But curiously, both of these priests somehow disappeared after the Miracle of the Sun, never to be heard from again, simply gone from history.
It's interesting that even today, skeptics continue to say that the whole thing was a hoax. There have been numerous books written on the great deception
that was "Fatima" -- how many parts of the various testimonies are in conflict or don't make sense when put together. But this should not be too surprising that there would be conflicting accounts because in everyday life whenever a crisis or unusual event happens, the testimony of various witnesses can be very different, even in contradiction to each other.