Questions on high altitude pressures

At low altitudes the rule of thumb is that a one thousand foot
increase in altitude results in a one inch of mercury decrease in
pressure; at least that is what happens when I turn the little knob on
my altimeter. Since commercial planes flight well into the FL300+
range, clearly that rule cannot hold at altitude as a plane taking off
at 29.92 inches would find itself in a vacuum at 29,900 feet above sea
level. Can someone with experience of high altitude flight expand on
my understanding of pressure variation?

Also, since the altimeter in the C182 I fly appears to incorporate
that rule of thumb, is it accurate at say, FL120, or is another kind
of altimeter needed for planes flying up there?

TIA