Re: honeymoon period. I think that the length of this period depends entirely on the species of bird, the care it got in the past, how long it was and the care it's receiving in the new house. If the bird is of an 'easy' species (the kind that bonds easily and deep with people), it's relatively healthy, was not severely neglected or abused at his previous home and the new home provides good care all around (good diet, good light quality and schedule, a steady daily routine and experienced handling), the honeymoon period is short BUT if the poor bird starts from minus zero (health, socialization, previous inadequate care, etc), it's of a 'difficult' species (like an IRN, for example), and the new owner is inexperienced and expects (and demands) too much, too soon of the bird, it will take much longer.
But, aside from this, I also think that there are two different periods at work when we rehome an adult animal. One is the honeymoon period and the other is the 'finding its place in the flock' period. The honeymoon period is the one where, as it was stated above by previous posters, the bird behaves so as not to call attention to itself until it feels relatively comfortable in its new surroundings, the other one is the one it needs in order to feel 100%, completely at ease with EVERYTHING - and part of this is the actual running of a couple of complete cycle of seasons. It seems to me that a bird needs to go through a couple of the four seasons in order for the new owner to be able to say: "OK, this is, pretty much, what it is" This doesn't mean that the bird will not change at all for the rest of its life, mind you! But it's the point when one can 'see' the actual personality of the bird.