When should I send my current civilization into decline?
Well, there is no perfect answer to this question, or else the game wouldn't be fun at all for anyone. But…

1) If you guess that the next turn, you won't make more points than this turn, no need to move, then it is preferable to use this turn to decline.

2) If you spot a "perfect civilization" (for the given situation) in the queue and need to take it before anyone gets the same idea, go for it!

I have some trouble answering your question with a straight answer for one reason: this aspect of the game is purely second guessing; whatever you do depends of what the others will do and vice-versa. Having a neighbour that wants to destroy your civilization or being the border line between two enemies is very different (I am not speaking about pure strategy here but about the more or less logical desires of the players).

This is to say: no, there is no perfect strategy, but points 1) and 2) may be good hints.