  Determining accurate and precise stellar ages is a major problem in
astrophysics. These determinations are either obtained through empirical
relations or model-dependent approaches. Currently, seismic modelling is one of
the best ways of providing accurate ages. However, current methods are affected
by simplifying assumptions concerning mixing processes. In this context,
providing new structural indicators which are less model-dependent and more
sensitive to such processes is crucial. We build a new indicator for core
conditions on the main sequence, which should be more sensitive to structural
differences and applicable to older stars than the indicator t presented in a
previous paper. We also wish to analyse the importance of the number and type
of modes for the inversion, as well as the impact of various constraints and
levels of accuracy in the forward modelling process that is used to obtain
reference models for the inversion. First, we present a method to obtain new
structural kernels and use them to build an indicator of central conditions in
stars and test it for various effects including atomic diffusion, various
initial helium abundances and metallicities, following the seismic inversion
method presented in our previous paper. We then study its accuracy for 7
different pulsation spectra including those of 16CygA and 16CygB and analyse
its dependence on the reference model by using different constraints and levels
of accuracy for its selection We observe that the inversion of the new
indicator using the SOLA method provides a good diagnostic for additional
mixing processes in central regions of stars. Its sensitivity allows us to test
for diffusive processes and chemical composition mismatch. We also observe that
octupole modes can improve the accuracy of the results, as well as modes of low
radial order.
