In the film I tell the story of how St Silverius was deposed in favour of the rascally Vigilius, whose unfortunate story shows him veering between placating his Imperial Master, Justinian, by condemning the controversial "Three Chapters" and holding to the doctrines taught by his predecessors. As John Julian Norwich says in his book Byzantium, the Early Years:
The Pope was now generally reviled throughout Western Christendom as a turncoat and an apostate. In Africa, indeed, the local bishops went further still and excommunicated him. p.149
Vigilius was appointed in 537 AD and St Silverius was probably killed in December 537, but Vigilius was not safe on his throne until the Goths were finally driven away from Rome in March of 538 and he was accepted by the clergy of Rome, which is why that year is taken by Protestant commentators as the beginning date for the prophetic period of 1260 years.
Daniel chapter 7 refers to a period of "a time, times and half a time". "Time" is a synonym for "year" and due to a peculiarity of Hebrew grammar, the word "times" can only mean two years. We are thus presented with a period of three and a half years, which is assumed to be the old Jewish lunar year of 360 days, so 3.5*360=1260.
Finally, Pope Pius VI was taken captive by the French general Louis Berthier in February 1798, which was indeed 1260 years after Vigilius. The prophecy would thus seem to have been fulfilled.
Naturally this interpretation is not accepted by Roman Catholics and even many modern Protestants are unaware of it. Nonetheless, as the Reverend E. Hoare, Canon of Canterbury Cathedral, said in his little book, Rome, Turkey and Jerusalem:
I have no time to discuss arguments and can merely state conclusions. All, therefore, that I can do now is to express my own convictions on two points:
1. That the little horn diverse from all the rest is the Papal power.
2. That the "time, times and dividing of a time", which is to be the limit of its power, stands in prophetic figure for 1260 years. p. 13
The reader is invited to make his own study of Daniel chapter seven. If he is a Christian, he will naturally assume that God is well able to fortell the future in detail, in which case he will, I think, be hard put to find a better solution to the prediction of "a time, times and a dividing of times".