  We study the reliability of the statistical background subtraction method for
computing the Ks-band luminosity function of cluster galaxies at z~1 using mock
Red-sequence Cluster Survey cluster catalogues constructed from GALFORM
semi-analytic galaxies. The underlying cluster luminosity function in the mocks
are compatible with recent estimates at z~1 by several authors. We simulate
different samples where the number of clusters with Ks-band photometry goes
from 5 to a maximum of 50, in order to find the most suitable observational
sample to carry out this study; the current observational status in the nIR
wavelength range has been reached using 5 real clusters at z~1. We compute the
composite luminosity function for several samples of galaxy clusters with
masses 1.5x10^14 M_sun assuming a flux limited, complete sample of galaxies
down to Ks=21.0 magnitudes. We find that the Schechter fit parameters Ks* and
alpha for a sample of galaxies with no redshift information are rather poorly
constrained if both parameters are allowed to vary freely; if alpha is fixed at
a fiducial value, then Ks* shows significantly improved stochastic
uncertainties but can be influenced by systematic deviations. We find a
significantly improved accuracy in the luminosity function parameters when
adding photometric redshift information for bright cluster galaxies. The
dwarf-to-giant ratios inferred from the luminosity functions of red-sequence
galaxies in the mock catalogue agree very well with the underlying values.
Finally, we find that in order to use estimates of Ks* to study the formation
redshift of cluster galaxies at z=1, the sample would need to contain 520 z~1
clusters, for an accuracy of 2 Gyr at the 68 per cent confidence level.
