If you examine the data at https://www.gapminder.org/tools/ you will find that the Gini coefficient does not really correlate well with much. Various indicators of political freedom or democratic process, spending on this-and-that, pensions, taxation, education, literacy, work force participation, etc. Examine it and you find that there are some little trends in regions, but that these do not survive world wide. For example, you might find that among sub-Saharan African countries there was a weak trend on some feature, but that this entirely disappears when other countries are brought in.
As well, the spread in the Gini coefficient within single culture regions is about the same size as it is world-wide. For example, the spread across Africa is similar to the spread across Europe is similar to the spread in Asia is similar to the spread in the Americas.
For example, there is an extremely weak and noisy correlation between hours worked per week and the Gini coef, higher working hours giving a slight trend to increased coef. But the noise is the same general size as the signal. And if one or two of the outliers were dropped (Ethiopia for example) the trend is non-existant.
Most especially, we don't see any region or culture hitting especially low or especially high. All have substantial range, and all vary over time.
So there does not seem to be any simple feature of a society that predicts the Gini coefficient. It seems to be the result of a large number of influences that are not readily captured in statistical analysis. And possibly in the interactions of those features.
Consider just one hypothetical example influence. Suppose that a particular country were attractive, for whatever reasons, for wealthy people to migrate to. One might suspect this would drive up the Gini coefficient, as "the rich" would be showing up in that country. If so, it's quite difficult to spot that country from the data. One might suspect that should be the USA. However, Brazil has a significantly higher coef.
So the conclusion is, the Gini coef does not correlate well with any easily identifiable single characteristic of a country. Particularly if you examine it over time. Possibly you could work out some complicated model of a culture that would consistantly hit low Gini coef values. It would be far more complicated than picking out a single parameter and trying to predict the coef from that. Probably it would be more than even two or three parameters.
By the way, there is a further conclusion. If a politician claims inequality is a severe problem, and that his pet program will allieviate it, he should be examined with some considerable suspicion. The data at hand indicates that inequality does not correlate well with any other societal indicator. Happiness, household income, life expectancy, level of education, nothing correlates. So it is a good question whether we should be particularly concerned about the Gini coef. And we should be suspicious whether his program will change it.