  The complexity of constraining the stellar initial mass function (IMF) in
early-type galaxies cannot be overstated, given the necessity of both very high
signal-to-noise (S/N) data and the difficulty of breaking the strong
degeneracies that occur among several stellar population parameters including
age, metallicity and elemental abundances. With this paper, the second in a
series, we present a detailed analysis of the biases that can occur when
retrieving the IMF shape by exploiting both optical and NIR IMF sensitive
spectral indices. As a test case, here we analyze data for the nearby galaxy
M89, for which we have high S/N spectroscopic data that cover the
3500-9000{\AA} spectral region and allow us to study the radial variation of
the stellar population properties out to 1 R_e. Carrying out parallel
simulations that mimic the retrieval of all the explored stellar parameters
from a known input model, we quantify the amount of bias at each step of our
analysis. From more general simulations we conclude that to accurately retrieve
the IMF, it is necessary not only to retrieve accurate estimates of the age and
metallicity, but also of all the elemental abundances that the spectral index
fits are sensitive to. With our analysis technique applied to M89, we find
consistency with a bottom-heavy IMF with a negative gradient from the center to
half R_e when using the Conroy et al. 2018 as well as Vazdekis et al. 2016
EMILES stellar population models. We find agreement both with a parallel full
spectral fitting of the same data and with literature results.
