I do not have the quote handy but Rutherford claimed to get messages from angels and so lots of times in regard to the 1935 date you will The Watchtower articles will say things like 'God’s light flashed up and it was revealed that…"
As far as 1914 goes, the JWs got that date from the Second Adventists who were on off-shoot of the Millerite movement of the 1840’s. The Second Adventists and the JWs are sort of theological cousins to the Seventh Day Adventists who also come out of the Millerite movement.
If you want an EXTREMELY DETAILED history of the development of the 1914 doctrine and how the JWs are actually in a whole lot of trouble with it (as it has sort of put them in a theological box). You need to read Carl O. Jonsson’s book “The Gentile Times Reconsidered”. This book is the result of a letter that Carl (a former JW elder) wrote to the Watchtower Society when he realized that there was a fatal flaw in the JWs calculations leading to 1914. Of course, Carl was eventually disfellowshipped and shunned for pointing this out to the JW leadership so he decided to write this book. You can get a copy of this book at the following link:
Also, to understand the significance of this date and how it props up the religious authority of the JW leadership, you might want to read the following article:
In short, if the JWs’ 1914 date is wrong than any claim the Watchtower Leadership has to being “God’s official spokesperson” crashes like a house of cards. It was, in fact, this realization that got me to quit listening to the JW leadership.
P.S. Here is another link that might help too: