  Let $(X,G)$ be a minimal equicontinuous dynamical system, where $X$ is a
compact metric space and $G$ some topological group acting on $X$. Under very
mild assumptions, we show that the class of regular almost automorphic
extensions of $(X,G)$ contains examples of tame but non-null systems as well as
non-tame ones. To do that, we first study the representation of almost
automorphic systems by means of semicocycles for general groups. Based on this
representation, we obtain examples of the above kind in well-studied families
of group actions. These include Toeplitz flows over $G$-odometers where $G$ is
countable and residually finite as well as symbolic extensions of irrational
rotations.
