I don't read reversals rigidly. For me, they don't mean the same thing every time but the fact that any card is reversed is always significant, it's just significant in a different way depending on the cards surrounding it etcetera. I do see the Page of Wands as a symbol of information, openness, sharing and making your meaning obvious. So a reversed Page would often be something I associate with withholding, silence, uncertainty or some kind of unwillingness to be frank.
“I have always believed, and I still believe, that whatever good or bad fortune may come our way we can always give it meaning and transform it into something of value.”
- Hermann Hesse