What do you mean by the "behavior"?

It looks as if you just answered the question after asking it.

Normally the Google Dance happens early on in your sites listing as Google tries to find a suitable place for your site. This normally happens after some kind of changes to your site such as starting to get more backlinks than before. Or maybe, the ratio of your backlinks aren't matching up to your normal growth or progression.

Naturally there's more to it but don't have the space to cover the whole reasons why and all.

I'm asking because I'm curious if there is a certain common pattern it will follow. For example, if a site were on page 2, then disappears, then reappears on page 6, is it predictable to say where it will go now, is it random, or does it have to do with a complicated algorithm factoring in your new backlinks to your site since a certain period of elapsed time?

Not one that I've ever seen or heard about.

There are so many ranking variables to take into account that every site is going to behave differently.

There is a definite occurrence at least once a month where everything gets misplaced and afterward it will all fall back in place again. We laugh about it at work as we've noticed this for years and have many sites where we watch it's ongoing placement. I've never noticed if it happens near the same time every month but it does happen at least once a month.

Thanks to everyone who answerd, I just wanted a confirmation on what was going on. ^^ I got my question answered too thanks to jasonmorgan.

If anyone else wants to drop in some info too, please feel free.

You can learn more about the behavior of the Google Dance here. Everything you ever needed to know about the Google Dance:

Intricacies of the Google Dance, by The Mysterious Marketer

People dont understand how Google works.

Google is not "one server" who has all the rankings and listing and presents them to everyone online.

Google consists of MANY, MANY data centers around the globe...and each of the data centers can have different results. There is zillions of bots crawling and indexing the web...and then the results are available at different data centers at different times, and they also differ according to your own location.

So..google dance is ALSO a result of the data centers synchronizing and updating, and it is perfectly normal that results vary...there is simply not ONE single source of data...and its all dynamic and constantly changes.

It does have any particular pattern. It just happens especially if there was any changes to your site or if your site is new.