  We use a version of the instant-form relativistic quantum mechanics of
composite systems to obtain the gravitational form factors of the pion in a
common approach to its electroweak and gravitational properties. In the
preceding work [arXiv:2010.11640] we formulated the mathematical background,
presented the principal scheme of calculation and testified the obtained
qualitative results to satisfy the general constraints given by the principles
of the theory of hadron structure. In the present work we give the detailed
calculation of the gravitational form factors in large range of momentum
transfer, their static limits and the slopes at zero value, the mean-square
mass and mechanical radii of the pion. Now we take into account the
qravitational structure of the constituent quarks. We show that the results are
almost insensitive to the type of the model two-quark wave function in a close
analogy to the case of the pion electromagnetic form factor. We present a
correct calculation of the form factor $D$ and corresponding matrix element of
the energy-momentum tensor, going beyond the scope of the modified impulse
approximation. Most of the parameters that we use for the calculation had been
fixed even earlier in our works on the pion electromagnetic form factors. The
only free parameter is the $D$-term of the constituent quark, which we fix by
fitting the result for the slope at zero of the normalized to pion $D$-term
form factor $D$ of pion, to a choosen experimental value.
