In supersymmetric extensions of the Standard Model, higgsino-like charginos and neutralinos are preferred to have masses of the order of the electroweak scale by naturalness arguments. Such light , and states can be almost mass degenerate, and their decays are then difficult to observe at colliders. In addition to the generic naturalness argument, light higgsinos are well motivated from a top-down perspective. For instance, they arise naturally in certain models of hybrid gauge-gravity mediation. In the present analysis, we study two benchmark points which have been derived in the framework of such a model, which exhibit mass differences of in the higgsino sector. For chargino-pair and neutralino associated production with initial-state photon radiation, we simulate the detector response and determine how accurately the small mass differences, the absolute masses and the cross sections can be measured at the International Linear Collider. Assuming that 500 fb(-1) has been collected at each of two beam-polarisations P(e (+),e (-))=(+/- 30 %,a"80 %), we find that the mass differences can be measured to 40-300 MeV, the cross sections to 2-5 %, and the absolute masses to 1.5-3.3 GeV, where the range of values correspond to the different scenarios and channels. Based on these observables we perform a parameter fit in the MSSM, from which we infer that the higgsino mass parameter mu can be measured to a precision of about Delta mu=2-7 GeV. For the electroweak gaugino mass parameters M (1), M (2), which are chosen in the multi-TeV range, a narrow region is compatible with the measurements. For both parameters independently, we can determine a lower bound.