  The appearance of segregated wurtzite Mg$_x$Zn$_{1-x}$O with low Mg content
in thin films with $x>0.3$ affected by phase separation, cannot be reliably
probed with crystallographic techniques owing to its embedded nanocrystalline
configuration. Here we show a high-pressure approach which exploits the
distinctive behaviors under pressure of wurtzite Mg$_x$Zn$_{1-x}$O thin films
with different Mg contents to unveil phase segregation for $x>0.3$. By using
ambient conditions photoluminescence (PL), and with optical absorption and PL
under high pressure for $x=0.3$ we show that the appearance of a segregated
wurtzite phase with a magnesium content of x $\sim$ 0.1 is inherent to the
wurtzite and rock-salt phase separation. We also show that the presence of
segregated wurtzite phase in oversaturated thin films phase is responsible for
the low-energy absorption tail observed above $x=0.3$ in our Mg$_x$Zn$_{1-x}$O
thin films. Our study has also allowed us to extend the concentration
dependence of the pressure coefficient of the band gap from the previous limit
of $x$ = 0.13 to $x \approx 0.3$ obtaining d$E_g$/d$P$ = 29 meV/GPa for
wurtzite with $x \approx 0.3$ and 25 meV/GPa for the segregated $x\approx 0.09$
wurtzite phase.
