sklearn.mixture.GMM) for classification. Turned out a bit easier than expected (yay for scikit-learn!), but for others, here is my implementation of a class that behaves like the other classifiers (eg. sklean.svm.SVC). All you need to decide is how many Gaussians you want to model your data with, and off you go.
Link to Github repo. A Jupyter notebook shows a sample use.
Why isn't something like this in sklearn yet? Well, turns out someone did propose it already (no surprise) in a much more general way: see this discussion on GitHub. (I myself was pointed there when I asked about my own code) My bit of code is far more primitive, but I hope easier to understand.