Forgive each other’s generally done at any time, do not have to wait a moment Ramadhan or `Eid. Because there is no hadith or atsar indicating direction.
But if we want to explore it further, why it appears the trend thus, one of his analysis is that it is the month of Ramadhan laundering sin. As word of the Prophet about it.
If Allah has promised forgiveness of sins, then stayed to figure out how to apologize to fellow human beings. The sins which are directly to God Almighty must have forgiven according to the promise of Allah SWT, but what about the sins to a fellow human?
Let alone the people who run Ramadhan, even those who were martyred though, if there is still the cradle of sin to others, still could not go to heaven. Therefore, let me be sure all the unforgivable sin, in addition to God for mercy in the month of Ramadhan, also apologized to fellow humans, to be more complete. Thus the background.
So although there is no specific proposition which shows that the Prophet SAW did forgive each other ahead of Ramadan, but there is nothing wrong when everyone else is doing. It should be not only on the momentum of Ramadhan alone, because the apology was made at anytime to anyone.
Ideally do not merely lip service to apologize or to forgive, but also resolve all matters. As for debts and other. So that when they entered the Ramadan, we are clean from all concerned to fellow human beings.
Forgive each other could be done anytime, on the eve of Ramadhan, after or even outside of that month. And it does not need us to issue a verdict bid, God if there is such a phenomenon, simply because there is no explicit propositions.