The neutron and its hypothetical mirror counterpart, a sterile state degenerate in mass, could spontaneously mix in a process much faster than the neutron β-decay. Two groups have performed a series of experiments in search of neutron – mirror-neutron (n - n′) oscillations. They reported no evidence, thereby setting stringent limits on the oscillation time τ_nn′. Later, these data sets have been further analyzed by Berezhiani et al.(2009-2017), and signals, compatible with n - n′ oscillations in the presence of mirror magnetic fields, have been reported. The Neutron Electric Dipole Moment Collaboration based at the Paul Scherrer Institute performed a new series of experiments to further test these signals. In this paper, we describe and motivate our choice of run configurations with an optimal filling time of 29 s, storage times of 180 s and 380 s, and applied magnetic fields of 10 μT and 20 μT. The choice of these run configurations ensures a reliable overlap in settings with the previous efforts and also improves the sensitivity to test the signals. We also elaborate on the technique of normalizing the neutron counts, making such a counting experiment at the ultra-cold neutron source at the Paul Scherrer Institute possible. Furthermore, the magnetic field characterization to meet the requirements of this n - n′ oscillation search is demonstrated. Finally, we show that this effort has a statistical sensitivity to n - n′ oscillations comparable to the current leading constraints for B′ = 0.