In this article, the capability of present (H.E.S.S., MAGIC, VERITAS) and planned (CTA) ground-based Cherenkov telescope systems for detecting angular anisotropies in the diffuse gamma-ray background is investigated. Following up on a study of the impact of instrumental characteristics (effective area, field of view, angular resolution, and background rejection efficiency), the first part examines the influence of different observational strategies, i.e. whether a single deep observation or a splitting over multiple shallow fields is preferred. In the second part, the sensitivity to anisotropies generated by self-annihilating dark matter is studied for different common dark matter models. We find that a relative contribution of ∼ 10% from dark matter annihilation to the extra-galactic diffuse gamma-ray background can be detected with planned configurations of CTA. In terms of the thermally-averaged self-annihilation cross section, the sensitivity of CTA corresponds to values below the thermal freeze-out expectation 〈σv〉 = 3 × 10-26 cm3 s-1 for dark matter particles lighter than ∼ 200 GeV. We stress the importance of constraining anisotropies from unresolved astrophysical sources with currently operating instruments already, as a novel and complementary method for investigating the properties of TeV sources.