There are at least three problems hidden in your question respectively observation.
The first is the light. All colours are partly products of light, they need light to be realized by those who should realize them (and by those who should not, the enemies). The intensity of light, the angle or direction of light respectively the body of the fish towards the light and the spectral composition of the light, its kelvin-type: all this changes the appearance of a fish that is accustomed by evolution to dark peat streams in rainforests. They are in need of the occasional sun beam and therefore turn their bodies and fins just for catching them. In the aquarium we have a steady light source of a steady composition and it is often too bright. We, the observer, see the colours from a fixed sidely angle and we see them according to our eyes and physical means of viewing them.
The second problem is that there are two types of colours. Those that are produced by pigments and those that are produced by structure. The red of our European Robin is of the first type; it is permanently to be seen from many angles and a bit dull. The blue of our European Bluethroat is of the second type: There is no blue pigment at all, but a special structure of the feathers. Being hit by light in special angles it appears strikingly and glitteringly blue. We have both types with the licorice. In their mostly to be seen normal appearance we mainly see its pigmentally caused colours. This includes the “black” of the lower part of the male nagyi-body. But in special situations and light-angles you see a second type of colours which is normally hidden by the pigments and the steady angle of light, and it is cause by the structure of the scales and scutes of the fish. That is the greenish or blueish tinge you decribe as appearing in certain special situations on the gills, the throat, in the fins.
But there is a third problem too, and it is the most interesting. There are not only two colour types and two appearances of a licorice gouramy – the dull normal colouring and the striking colouring in courtship and display – but there are more. One very effective colouring is that for aggression which intensifies the main colours distinctly. You can provoke it by using a mirror. There are some photos of licorice gouramies in this aggressive mood that have become possible by use of this means. And there is the colouring caused by situations of fear: a more scattered picture of a reduced apperance of the usual stripes mixed with vertical structures (reminding a bit at the colours of the offspring that especially must be prevented from being found by hungry other fish and kingfishers!). There are many photos showing us our fish coloured like this. Most photos taken shortly after the catch from the natural habitat are of this type. Many photos showing them in special photo-tanks without enough structures to hide and the light being too bright either. In the aquarium we don’t see this type very often since we omit the aggressors from the small tanks and the fish become rather quickly used to its permanent outfit and structure.
At least these four types of colouring must be distinguished. And we often see a certain mixture of all of them, at least for some seconds before it changes to one clear type. It is one of the problems of the many photos of our fish that they mix all these types and show them in different situations, often dominated by the duller types, but sometimes mingled with the striking colours of display and aggression, too. Many new friends send us photos and ask: What species is that? From those photos it is often impossible to say, not only because there are these many bintan-like forms in trade or because we see females or males in their normal appearance, but often because we see fish not yet grown up or not yet accustomed to their new home.