  Within the framework of the scalar-tensor theory (STT), its second
post-Newtonian (2PN) approximation is obtained with Chandrasekhar's approach.
By focusing on an $N$-point-masses system as the first step, we reduce the
metric to its 2PN form for light propagation. Unlike previous works, at 2PN
order, we abandon the hierarchized hypothesis and do not assume two
parametrized post-Newtonian (PPN) parameters $\gamma$ and $\beta$ to be unity.
We find that although there exist $\gamma$ and $\beta$ in the 2PN metric, only
$\gamma$ appears in the 2PN equations of light. As a simple example for
applications, a gauge-invariant angle between the directions of two incoming
photons for a differential measurement is investigated after the light
trajectory is solved in a static and spherically symmetric spacetime. It shows
the deviation from the general relativity (GR) $\delta\theta_{\mathrm{STT}}$
does \emph{not} depend on $\beta$ even at 2PN level in this circumstance, which
is consistent with previous results. A more complicated application is light
deflection in a 2-point-masses system. We consider a case that the light
propagation time is much less than the time scale of its orbital motion and
thus treat it as a static system. The 2-body effect at 2PN level originating
from relaxing the hierarchized hypothesis is calculated. Our analysis shows the
2PN 2-body effect in the Solar System is one order of magnitude less than
future $\sim 1$ nas experiments, while this effect could be comparable with 1PN
component of $\delta\theta_{\mathrm{STT}}$ in a binary system with two Sun-like
stars and separation by $\sim 0.1$ AU if an experiment would be able to measure
$\gamma-1$ down to $\sim 10^{-6}$.
