Hi Jillian,
What cichlids do you have that are doing this?
Are they the same sex and species?
It sounds to me like one of two things.
It could be a dominance display.Two cichlids acting like this can be the start of a dominance dispute.This kind of behaviour can be the first signs of future aggression.
Or,it could be courtship behaviour. I have seen the behaviour you describe in cichlids many times when two fish begin to pair up.
It's hard to be definite without seeing it and that's why I don't think you will find such a list.
A lot of cichlids will behave in ways that can have the same appearance but mean more than one thing.
Courtship and a aggressive displays can look the same for example.
A lot of other behaviour is often linked to an illness or parasite or poor tank maintenance. These will be named and described as a symptom,so will already be categorised in health guides.
I also think cichlids are complex and diverse.I would be sceptical about any definite generalisation pin pointing a behavioural trait to one specific act.
I've seen this in two separate species. The first time was in the wild in a clear creek in Austin Texas. They were Texas cichlids and I had trained them to come up to me for food. There was a group of them and one particular fish singled out another and performed the slow wobble. I couldn't tell sexes, but they were both medium sized adults.
The second time was with two Paratilapia (bleekeri or polleni, whatev's). I had just introduced the newbie and the established fish did this. Again, I'm not sure of sexes, still learning.
So it could be a dominance thing or a mating thing. The Texas cichlids did it during the mating season. (I did see fry in the weeks before.) I was hoping for a name of this very obvious behavior.