Given a dynamical system (that is, for me, a group $G$ acting by homeomorphisms on a compact Hausdorff space $X$), the Ellis group (which can be defined in terms of the universal minimal flow (as here), or just as the ideal group of the enveloping semigroup of the dynamical system) has a natural compact $T_1$ topology, which makes it a semitopological group.
I've seen claims that the topology is typically not $T_2$, but no examples. Are there any specific examples where it is not hard to see that the Ellis group is not Hausdorff?